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5 The Arbitrage-Free Value of a Eurobond Denote the arbitrage-free price of the defaultable zero coupon bond with (net) maturity T by F (T ) and the standard normal distribution function evaluated at z by N (z). 7) −k − √ 2 Ξ Ξ 2 V0 κ(0, T ) = ln def Ξ1 − Ξ2 σ2 2 1 T θ2 + 2 T − (1 − exp (−λT )) + (1 − exp (−2λT )) λ λ 2λ σ 1 2ρθ T − (1 − exp (−λT )) λ λ = def = def = Proof: At the outset some motivation is given. 314ff]. The expected payoff of the defaultable zero bond under the equivalent martingale measure has to be calculated.
1997). Stochastische Methoden im Risikomanagement des Kreditportfolios, Oehler. Risk, C. (1997). A credit risk management framework, Technical report, Credit Suisse Financial Products. Schmid, B. (1997). Creditmetrics, Solutions 1(3-4): 35–53. Sharpe, W. (1964). Capital asset prices: A theory of market equilibrium under conditions of risk, Journal of Finance 19. Vasicek, O. A. (1997). Credit valuation, Net Exposure 1. Wilson, T. (1997). Portfolio credit risk (i+ii), Risk Magazine 10. 1 Introduction The problem of estimating volatility is one of the most important topics in modern finance.
Pagan, A. (1996). The econometrics of financial markets, J. Empirical Finance 3: 15–102. Shiryaev, A. (1999). Essentials of stochastic finance, Advanced Series of Statistical Science & Applied Probability 3. World Scientific. Taylor, S. (1986). Modelling financial time series, J. Wiley & Sons. 1 Introduction It had been a widely held belief that the debt crisis of the 1980s was over when the Mexican crisis at the end of 1994, the Asian crisis in 1997, and the Russian crisis in 1998 made clear that highly indebted developing countries remain vulnerable.