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1
A Balance Sheet Approach for Sovereign Debt
Dan Galai*, Yoram Landskroner**, Alon Raviv and Zvi Wiener***
Jan-2011
Abstract
A sovereign that is issuing debt denominated in foreign currency is exposed to a mismatch between the value of its assets that can be used to serve the debt, denominated in local currency, and the value of its liability. During economic crisis, when the probability of default by the sovereign increases, there is a tendency for the exchange rate to experience sudden shock. Such a relationship has been observed in most of the recent financial crises in emerging markets (for example, in the East Asian crisis of 1997 and the Russian debt crisis of 1998).
In this paper we develop a structural model for pricing sovereign debt that is denominated in foreign currency where the effect of local economic crisis on the exchange rate is considered through a state-dependent jump intensity variable that is sensitive to the distance of default of the sovereign debt. The presented pricing model can produce a higher credit spread than the classical Merton-based approach (1974) for risky debt. The model can help traders, risk managers, accountants, and policymakers who are interested in more accurately evaluating the fair value of sovereign debt that is denominated in foreign currency.
Keywords: exchange rate, sovereign debt, jump diffusion, asset pricing,
JEL codes: G12; G13; G15
Corresponding author: Alon Raviv, Brandeis University, International Business School, Mailstop 32, Waltham, MA
02454‐9110, Tel: +1 (781)‐736‐2249. E‐mail: [email protected]
* School of Business Administration, The Hebrew University, Jerusalem, Israel, 91905, Email: Dan@sigma‐pcm.co.il
**The Center for Academic Studies and the Stern School of Business, New York University, E‐mail:
***School of Business Administration, The Hebrew University, Jerusalem, Israel, 91905, Tel: +972‐2‐588‐3049. E‐
mail: [email protected]
Electronic copy available at: http://ssrn.com/abstract=1740253
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1. Introduction
The risk of sovereign bonds has traditionally been perceived as more prevalent in emerging
markets, where most of the issued debt is denominated in foreign currency, and where usually a
local real economic crisis is often associated with a currency crisis. For example, recent
recessions attributed to currency crises include the 1994 economic crisis in Mexico, the 1997
Asian financial crisis, the 1998 Russian financial crisis, and the Argentine economic crisis
(1999-2002).
In this paper we develop a structural model for pricing sovereign debt that is denominated
in foreign currency where the effect of exchange rate crisis, in the event of a country’s real
economic crisis, is considered through a state-dependent jump intensity variable that is related to
the probability of financial distress.
Country risk is the risk that a country will be unable to service its external debt due to an
inability to generate sufficient foreign exchange. Therefore, a common practice for pricing
sovereign debt is to truck the Black Scholes (1973) and Merton (1974) structural model for
pricing corporate debt and to assume an analogy between the value of the firm’s assets and some
macro fundamental index of the economy, which is strongly aligned with the sovereign’s ability
to generate cash to service its debt in the future. According to these models, with some variation,
in the case that the fundamental value of the economy exceeds its debt at maturity, the
debtholders are fully paid. Otherwise, if the fundamental value is below the debt value, the
debtholders receive the residual value of the fundamental. As such, the debt value is identical to
3
the value of a risk-free debt minus the value of a put option on the value of the fundamental of
the economy with a strike price that is equal to the face value of debt.1
Since the local debt market is relatively scarce in most emerging markets, it is typical for
such a sovereign to issue debt that is denominated in foreign currency. Therefore, a currency
mismatch is introduced between the assets side, where most of the generated income is
denominated in local currency, and the liabilities side, which is denominated mostly in foreign
currency. The issue of “currency mismatch,” i.e., discrepancies between the direct currency
composition of assets and liabilities held by corporations and sovereigns, has attracted the
attention of academics and policymakers. Currency mismatch is often singled out as an important
factor in financial crises, particularly in developing economies.2
Galai and Wiener (2009) noted that to correctly price sovereign debt that is denominated
in foreign currency, the mechanism of the exchange rate should be taken into account as well.
Therefore, a two-factor model is suggested in which both the exchange rate and the fundamental
of the economy follow a geometric Brownian motion and a correlation between the returns is
considered. They applied the model to the pricing of corporate bonds denominated in foreign
currency by using the change of numeraire technique.
An important aspect in which sovereign debt differs from corporate debt is the effect of
the macroeconomic environment on the exchange rate. In modeling corporate debt, the
underlying asset value may be affected by exchange rate movements, but exchange rates are
1 In the financial literature until recently, a country’s GDP or its foreign reserve served as the underlying asset representing a country’s ability to pay back its debt. Hilscher and Nosbusch (2010) suggest using some fundamental index of the economy that best represents the ability of the country to pay back its debt. This fundamental is not limited to the above-mentioned indexes.
2 See Caballero and Krishnamurthy, 2005; Catao and Sutton, 2002; Duffie, Pederson, and Singleton, 2003; Gibson and Sundaresan, 2001; Gray, Merton, and Bodie, 2007; Longstaff, Pan, Pedersen, and Singleton, 2007; and Weigel and Gemmill, 2006.
4
rarely affected by a specific firm’s asset value. However, when modeling sovereign debt, a
country’s exchange rate is strongly affected by the economic fundamentals. In recent years, a
new generation of foreign exchange rate models has been developed to account for the cross
effects between the fundamental of the economy and the exchange rate. The literature stressed
the role of balance sheet effects in explaining the contradictory effect of depreciations in
explaining exchange rate overshooting. Cavallo, Kisselev, Perri, and Roubini (2005, hereafter
CKPR) described a shock that forces both a depreciation of the exchange rate and an adjustment
of the portfolio holdings of the country. An immediate depreciation of the exchange rate causes
the country to fire-sell domestic stocks to buy back some external debt in an attempt to comply
with the margin constraint. However, the fire sale often depresses domestic stock prices further
relative to the foreign currency debt, and by the end, the country is left with an even larger
depreciation and a net loss of wealth. Such shocks have been observed in the East Asian
financial crisis of 1997, the Russian bond default of 1998, and other currency crises.
A similar mechanism for explaining these links, but with more precision regarding the
different stages of economic crisis associated with currency crisis in emerging markets, has been
modeled by Mendoza and Smith (2006). According to their framework, where the economy’s
debt is “sufficiently high,” the financial distress triggers collateral constraints and forces
domestic agents to fire-sell assets to foreign traders. These traders are slow to adjust their
portfolios because of trading costs, and as a result, asset prices fall.
In this paper we develop a framework for pricing sovereign debt that is consistent with
the CSPR model and other papers that belong to the balance sheet approach, where the
probability of a jump in the exchange rate depends on the distance to default of the sovereign. As
the distance between the country fundamental of the economy and the value of debt decreases,
5
the probability of a positive jump in the exchange rate increases as well. The distance to default
is measured by using a first passage model that takes into account both the leverage ratio (the
ratio between the discounted value of debt and the value of the fundamental) and the volatility
that affects this probability. Thus we address the effect of exchange rate overshooting in a
currency crisis, where the probability of currency depreciation may increase exponentially as the
country fundamental gets close to the debt value.
To capture the effect of real economic distress on the exchange rate we introduce a new
state variable that is sensitive to the probability of default. When the probability of default is low,
the state variable receives values close to zero. However, when this probability crosses some
upper threshold, the value of the state variable may jump and the probability of a sudden
depreciation of the exchange rate gets closer to some upper value. For example, when the
probability of default is below 3%, the probability of a positive jump event of the exchange rate
in the coming year is close to zero, but when the probability of default is above this level, the
probability of a jump event (the intensity of a jump event) reaches its maximum level: a 25%
chance of a jump in the coming year.
It is well documented that structural models of default that are calibrated to historical
default rates and restricted to “reasonable” risk-premia specifications generate counterfactually
low yield spreads for investment-grade debt, especially for debt of short maturity (Mason and
Rosenfeld, 1984, Huang and Huang, 2002, and Eom, Helwege, and Huang, 2003). These
deviations are even higher during periods of financial crisis. Using our model, one can better
price sovereign debt by accounting for the potential connection between the exchange rate, the
state of the economy, and the tendency of the exchange rate to depreciate in a time of local
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economic crisis. Therefore, our model can produce a higher credit spread for any given level of
parameters compared to the traditional structural models for pricing sovereign debt.
Although it has been widely documented that FX returns exhibit jumps (see, for example,
Jorion, 1998), our paper is the first to our knowledge that connects the sovereign assets and
liability position with the frequency of the jump. This is done by introducing a state-dependent
jump intensity variable that is affected each time by the distance of default of the sovereign. In
its turn, the distance to default of a sovereign is sensitive both to the volatility of the fundamental
of the economy and the ratio between the value of assets and liabilities at any time.
The structure of the paper is as follows: section 2 presents a basic model for pricing
sovereign debt and our assumptions; section 3 presents our numerical analysis; section 4
summarizes and concludes.
2. The Model
In a conventional setting, the process for the foreign currency exchange rate and the country
economic fundamental can be defined by two correlated Geometrical Brownian Motion
processes as in Galai and Wiener (2009). Thus, the processes of the economic fundamental, V ,
and the exchange rate between the local currency and the currency in which the debt is
denominated in, can be defined as follow:
VV dWrdVV
dV (1)
7
SSdWdtrfr
S
dS )( (2)
where r is the local risk-free rate and rf is the foreign risk-free interest rate. It is assumed that
2S and 2
V , which are respectively the instantaneous variances of the rate of return of the
underlying exchange rate, ,S and the fundamental of the economy, V , are constants. SdW and
VdW are standard Wiener processes with correlation given by dtdWdW SVVS .
The value of a zero coupon bond, which is issued by the foreign sovereign and
denominated in foreign currency, has a face value of F, matures at time, T, and has two sources
of value. The first is its value at maturity, assuming the value of the fundamental in terms of the
foreign currency is above the face value of debt, and thus the face value of F is paid in full to the
bondholder. The second is the value of the fundamental in terms of the foreign currency,
)( TT SV , in case its value at maturity is below the face value of debt. The payoff for the
debtholder at debt maturity can be expressed as:
)0,max(),/min( TTTTT SVFFFSVB (3)
The pricing equation can either be solved by using the change of numeraire technique, in which a
new stochastic variable that is equal to the quotient between the fundamental and the exchange
rate is introduced, or by using some numerical solution.
The process depicted above, however, does not consider the exchange rate overshooting
in a real economic crisis, as described in CKPR. In this paper we try to simplify the approach in
8
order to use it in a practical pricing model; therefore, we consider one simple possible shock, in
which deterioration in the state of the economy can lead to sudden exchange rate devaluation.
To simulate such exchange rate overshooting, we introduce a jump in the exchange rate
process where the intensity of the jump is dictated by a state-dependent variable that is linked to
the risk neutral probability of default, i.e., the first passage time in the coming year when the
value of the fundamental would be below the face value of debt. The value of the state-
dependent jump intensity variable is calculated in two steps. First, we calculate at any time the
first passage probability that the value of the fundamental would touch the face value of the debt
in the coming year. The probability, tPd , receives a value between zero and one as long as the
value of the fundamental is above the face value of debt. At the second step, we use an
exponential function that connects the probability of default and the intensity of the jump. This is
an increasing function of the first passage probability. However, when some level is reached, the
intensity increases exponentially until it reaches the chosen maximum intensity level.
If the threshold is equal to the face value of debt denominated in the foreign currency, F ,
then the risk neutral probability for the first passage time untill maturity T, that the fundamental
would touch the threshold, can be derived analytically. This value is equivalent to the probability
that the running minimum of the log-asset value at maturity, T , would be below the adjusted
default threshold )/ln( txF , where ttt SVx / . As presented in Giesecke (2003), employing the
fact that the distribution of the minimum is inverse Gaussian, and setting )2( 2xrm , where
the variance of the process is set to VSSVx 2222 (as in Galai and Wiener, 2009), we
can write this probability as:
9
T
mTxFNe
T
mTxFNPd
x
t
xFm
x
tt
x
lnln 2
ln2
(4)
where N is the standard normal cumulative distribution function. When the value of the
fundamental is below the face value of debt at any time before maturity, the probability is fixed
to one.
The state-dependent jump intensity variable at any time, t , is an exponential function of
the probability of financial distress at the coming next year, tPd . The chosen setting enables us
to calibrate the model such that the probability of a sudden devaluation (a jump of the exchange
rate) is strongly related to insolvency of the issuing sovereign. Thus, the model can enable a non-
linear relationship between the fundamental of the economy and exchange rates, in contrast to
the common models, which assume a linear relationship by using only the correlation terms. The
exponential state variable is expressed as:
e
e tPd
t (5)
where the parameter determines the probability of default from which the exponential
function would start to jump from levels that are close to zero into the maximum possible level,
and the parameter is just a scale parameter that determines the maximum probability of a
jump in a certain time. Figure (1) presents the level of the state-dependent jump parameter for
10
different levels of default probability. As the parameter increases, the state-dependent jump
intensity variable gets closer to one for a higher level of default probability.3
Figure (1) presents the relationship between the probability of default and the jump
intensity state-dependent parameters. As the probability of default increases, the jump intensity
also increases. Moreover, the sensitivity of the jump intensity to the default probability can be
controlled through the parameter . When the parameter is equal to two, the jump intensity
parameter is close to zero whenever the default probability is below 40%. However, when is
equal to six, the jump intensity parameter is close to zero for any level of default probability that
is below 60%.
After defining the state-dependent jump intensity variable, we would redefine the foreign
exchange process as follow:
qK +)( SS dWdtrfrS
dS (6)
where:
dt
dt
t
t
ofy probabilit with 1
-1 ofy probabilit with 0q (7)
3 A possible extension is to relate not just to the probability of default as a trigger for a jump event, but also to the
time spent in financial distress similar to the framework of Galai, Raviv, and Wiener (2007).
11
and K is the jump size that is measured as a proportional increase in exchange rate; q is the
Poisson distribution; and λt is the jump intensity state variable that changes over time according
to the default probability as described in equations (4) and (5).4 The notation S− means that there
is a jump.
Figure (2) and Figure (3) demonstrate the stochastic process for two typical simulation
paths. The figures present simulation paths for both the value of the fundamental of the economy
and the value of debt in terms of the local currency. In both figures, the parameter is equal to
two and therefore for a probability of default below 40%, the intensity parameter would receive
values of zero. In Figure (2), the simulation path of the fundamental of the economy is always far
enough from the face value of debt denominated in foreign currency; therefore, the probability of
default is always below 40% and no jump events are observed. However, Figure (3) presents a
situation in which the value of the fundamental of the economy is getting close to the value of
the face value of debt and, while the probability of default is above 40%, three jump events are
observed.
3. Numerical Examples and Illustrations
In this section we illustrate our approach by using numerical examples. We first solve the
problem using a Monte Carlo simulation and then, similar to Galai and Wiener (2009), who
4 The size of the jump event, K, usually is defined by some normal distribution, where the average size of the jump
and its standard deviation are defined. However, in order not to complicate the idea and to focus on our novel
contribution, we define the jump size as constant.
12
analyzed corporate debt denominated in foreign currency, we demonstrate the pricing of zero
coupon bonds.
In our Monte Carlo simulation we use 100,000 simulation paths, and both the
fundamental of the economy and the exchange rate process are sampled monthly. While
exchange rates are traded in almost continuous time, new information regarding the value of the
fundamental is revealed more discreetly, when some leading indicators of the economy are
published, usually on a monthly or even quarterly frequency. Therefore, to account for the effect
of financial crisis on exchange rate shocks, it is reasonable to sample both the exchange rate and
the fundamental of the economy on a monthly basis frequency. We checked for robustness, and
our results are steady for the first four digits of the calculated credit spread.
We begin to explore the pricing model by assuming a base case similar to Galai and
Wiener (2009), where the fundamental of the economy is equal to V=100 in terms of the local
currency and the sovereign is issuing a pure discount (zero coupon) bond denominated in US
dollars with a current value of B=$70, maturing in T=5 years. The standard deviation of the
fundamental rate of return (in local currency) is Х=20% and the standard deviation of the
returns of the exchange rate is 6%. We further assume that both the local and the foreign risk-
free rate is 5%. The exchange rate between the local currency and the US dollar is equal to S0=1.
The face value of debt that makes the value of debt being equal to $70, in the absence of a jump
term and correlation of zero between the returns of the exchange rate and the returns on the
sovereign, is $99.4, where the credit spread is equal to 202bp, as reported by Galai and Wiener
(2009) for identical data. However, keeping all else equal and introducing our novel state-
dependent jump process, with a constant jump size of 10% and jump intensity parameters of
=0.5 and =2, the face value of debt that makes the current debt equal to $70 is now increased
13
to $122.5, where the credit spread is equal to 622bp. As can be seen from Figure (1), these higher
values take into account that as the risk neutral probability of default at any time gets closer to
40%, there is 50% of one jump event (determined by the parameter ) in the coming year. By
taking the event of currency shock as modeled, the credit spread is higher by 419bp than the
previous case. Of course, the size of the spread can be controlled by modeling the maximum
frequency of the jump (the parameter ).
Figure (4) presents the credit spread for different levels of the fundamental and different
jump sizes. All the other data are similar to the base case. When the jump size is equal to zero,
the model is a special case of the two correlated assets with Geometric Brownian motion and no
jump term. It is clear that for a low leverage ratio (i.e., a high level of the fundamental of the
economy), the state-dependent jump intensity variable receives a relatively low value in most
cases and, therefore, the jump element has almost no effect on the pricing. However, when
leverage is relatively high, the probability of a jump event increases and the suggested model can
lead to yield spreads that are significantly different. For example, when the value of the
fundamental is equal to 100, the credit spread of a model with no jump term is equal to 198bp,
while the credit spread of models with 3% and 6% jump sizes are equal to 245bp and 303bp,
respectively. When the value of the fundamental of the economy is relatively high and equal to
120, the spread in the case of no jump term is equal to 107bp, while the spread for a jump term
of 3% and 6% is equal to 136bp and 171bp, respectively.
Figures (5) and (6) show the credit spreads when the volatility of the exchange rates is
either 6% or 12%. However, in Figure (5) there is no jump term, while in Figure (6) we
introduce a jump term according to the base case parameters. In both cases, the credit spread
decreases with the value of the fundamental of the economy and increases with the volatility of
14
the exchange rates. However, the change in the exchange rate volatility from 6% to 12% in the
case with a jump term has almost no effect on credit spread for low levels of the fundamental and
the dominant component is the jump term itself. Moreover, for relatively high leverage ratio, in
which a jump would certainly occur (the economy is in a kind of “default” already), the
fundamental with the higher volatility has a lower credit spread since the high level of volatility
increases the probability of being away from the area in which frequent devaluation of the
currency occurs.
4. Summary and Conclusions Sovereign bonds denominated in foreign currency may create a mismatch between the value of
the assets that can serve the debt, usually denominated in local currency, and the value of
liabilities. During economic crisis, when the probability of default of the sovereign increases,
there is a tendency for sudden shocks in the exchange rate that are caused by the need to fire-sell
domestic stocks to buy back some external debt in an attempt to comply with the margin
constraint. Such a relationship has been observed in most of the recent financial crises in
emerging markets. For example, recent recessions attributed to currency crises include the 1994
economic crisis in Mexico, the 1997 Asian financial crisis, the 1998 Russian financial crisis, and
the 1999-2002 Argentine economic crisis. In this paper we developed a structural model for
pricing sovereign debt that is denominated in foreign currency where the effect of exchange rate
overshooting in the event of a country’s default is considered through a state-dependent jump
intensity variable that is sensitive to the distance of default of the sovereign debt.
15
While previous models recognized the existence of a jump process in foreign exchange
rates, and described pricing models for FX derivatives where a jump is taken into account, none
of them related the economic causality that affects those jumps. The presented model is a first
attempt to create a balance sheet approach in which the frequency of the jump is strongly related
to the distance of default between a country’s ability to serve its debt and the value of its debt
denominated in foreign currency. The method can be expanded to many other applications , as
the pricing of derivatives on foreign currency in illiquid markets as well as calibrating the model
parameters to sovereign debt CDS.
16
References Black, F., and M. Scholes, 1973, “The Pricing of Options and Corporate Liabilities” Journal of
Political Economy, 81 (3), 637–654.
Caballero, R. J., and A. Krishnamurthy, 2005, “Excessive Dollar Debt: Financial Development
and Underinsurance,” Journal of Finance 58(2), 867-793.
Catao, L. and B. Sutton, 2002, “Sovereign Default: The Role of Volatility,” IMF Working Paper
WP/02/149.
Cavallo, M, K. Kisselev, F. Perri, and N. Roubini, 2002, “Exchange Rate Overshooting and the
Cost of Floating,” Mimeo. New York University.
Duffie, D., L. H. Pedersen, and K. J. Singleton, 2003, “Modeling Sovereign Yield Spreads: A
Case Study of Russian Debt,” Journal of Finance, 119-159.
Eom, Y.H., J. Helwege, and J.Z. Huang, 2004, Structural Models of Corporate Bond Pricing: An
Empirical Analysis,” Review of Financial Studies, 17, 499–544.
Galai, D. and Z., Wiener, 2009, “Credit Risk Spreads in Local and Foreign Currencies,” IMF
Working paper WP/09/11, International Monetary Fund, Washington, DC.
Galai, D., A. Raviv, and Z., Wiener, 2007, “Liquidation triggers and the valuation of equity and
debt,” Journal of Banking and Finance, 31, 3604-3620.
Gibson, R., and S. Sundaresan, 2001, “A Model of Sovereign Borrowing and Sovereign Yield
Spreads,” Working Paper, Columbia University.
Giesecke, K, 2003, “Credit Risk Modeling and Valuation: An Introduction,” Working Paper,
School of Operations Research and Industrial Engineering, Cornell University.
Gray, D.F., R.C. Merton, and Z. Bodie, 2007, “A Contingent Claims Approach to Measuring and
Managing Sovereign Credit Risk”, Journal of Investment Management 5, 1-24.
17
Hilscher, J., and Y. Nosbusch, 2010, “Determinants of Sovereign Risk: Macroeconomic
Fundamentals and the Pricing of Sovereign Debt”, Review of Finance 14, 235-262.
Jones, E.P., S.P. Mason, and E. Rosenfeld, 1984, “Contingent Claims Analysis of Corporate
Capital Structures: An Empirical Investigation,” Journal of Finance, 39, 611–625.
Jorion, P., 1988, “On Jump Processes in the Foreign Exchange and Stock Markets,” Review of
Financial Studies, 1, 427-445.
Longstaff, F.A., J. Pan, L.H. Pederson, and K.J. Singleton, 2007, “How Sovereign Is Sovereign
Credit Risk?” NBER Working Paper No. 13658.
Mendoza, E.G., and K.A., Smith, 2006, “Quantitative Implications of a Debt Deflation Theory of
Sudden Stops and Asset Prices.” Journal of International Economics, 70, pp. 82–114.
Merton, R.C., 1974, “On the Pricing of Corporate Debt: The Risk Structure of Interest Rates,”
Journal of Finance, 29, 449-70.
18
Figure (1): The value of the state-dependent jump intensity parameter for
different probabilities of default and function parameters.
The figure presents the state-dependent jump parameter, , for different probabilities of defaults
(ranging from zero to one) and different levels for the parameters and of the exponential
function (equation 5).
19
Figure (2): A simulation path where the distance between the value of the
fundamental, denominated in local currency, and the face value of debt is
relatively high
The upper panel presents a ten-year simulation path for the value of the fundamental, denominated in the local currency, and the face value of the debt denominated in the foreign currency. The risk-free rate is equal to 5%, the fundamental volatility and the exchange rate volatility are equal to 20% and 6%, respectively, and the correlation between them is equal to zero. The face value of debt is equal to 70 and the initial values of the exchange rate and the fundamental are equal to 1 and 100, respectively. The lower panel presents the distance to default, jump events, and the state-dependent jump intensity variable when =0.5 and =2.
0
50
100
150
200
250
300
350
400
450
0 1 2 3 4 5 6 7 8 9 10
The value of assets and debt
Years
The sovereign fundamental value Face value in local currency
0%
5%
10%
15%
20%
25%
30%
35%
40%
0 1 2 3 4 5 6 7 8 9 10
Percents
Years
Jump event First passage probability
20
Figure (3): A simulation path where the distance between the value of the
fundamental, denominated in local currency, and the face value of debt is
relatively low
All parameters are identical to those in Figure (2).
0
50
100
150
200
250
0 1 2 3 4 5 6 7 8 9 10
The value of assets and de
bt
Years
The sovereign fundamental value Face value in local currency
Jumps events
0
0.2
0.4
0.6
0.8
1
0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00
Jump event First passage probability The state dependent jump intensity
21
Figure (4): The credit spread of a sovereign debt for different levels of the
fundamental of the economy and jump size.
The jump size receives a value between 0% and 10% of the logarithmic value of the exchange rate, the value of the fundamental receives a value between 100 and 165, and all other parameters are identical to those in Figure (2).
22
Figure (5): The credit spread of a sovereign debt for different levels of the
fundamental of the economy and assets volatility when there is no jump term.
The jump size receives a value of 0%, the value of the fundamental receives a value between 90 and 110, and exchange rate volatility can be either 6% or 12%. All the other parameters are identical to those in Figure (2).
23
Figure (6): The credit spread of a sovereign debt for different levels of the
fundamental of the economy and assets volatility with a jump term.
The jump size receives a value between zero and 10%, the value of the fundamental receives a value between 70 and 110, and exchange rate volatility can be either 6% or 12%. All the other parameters are identical to those in Figure (2).
