A Simple Novel Approach to Valuing Risky Zero Coupon Bond in a Markov Regime Switching Economy
- 120 Downloads
We have addressed the problem of pricing risky zero coupon bond in the framework of Longstaff and Schwartz structural type model by pricing it as a Down-and-Out European Barrier Call option on the company’s asset-debt ratio assuming Markov regime switching economy. The growth rate and the volatility of the stochastic asset debt ratio is driven by a continuous time Markov chain which signifies state of the economy. Regime Switching renders market incomplete and selection of a Equivalent martingale measure (EMM) becomes a subtle issue. We price the zero coupon risky bond utilizing the powerful technique of Risk Minimizing hedging of the underlying Barrier option under the so called “Risk Minimal” martingale measure via computing the bond default probability.
KeywordsRisky zero coupon bond Longstaff and Schwartz model Markov modulated economy Down-and-Out European Barrier Call option Risk Minimal martingale measure Bond default probability
AMS 2000 Subject Classifications91B28 91B70
Unable to display preview. Download preview PDF.
- Basak G, Ghosh MK, Goswami A (2008) Exotic options in a Markov modulated market (Preprint)Google Scholar
- Di Masi GB, Kabanov YM, Runggaldier WJ (1994) Mean-variance hedging of options on stocks with Markov volatility. Theory Probab Appl 39:173–181Google Scholar
- Föllmer H, Schweizer M (1990) Hedging of contingent claims under incomplete information. In: Davis MHA, Elliott RJ (eds) Applied stochastic analysis. Stochastics Monographs, vol 5. Gordon & Breach, New York, pp 389–414Google Scholar
- Föllmer H, Sondermann D (1986) Hedging of non-redundant contingent claims. In: Hildenbrand W, Mas-Colell A (eds) Contributions to mathematical economics, North-Holland, pp 205–223Google Scholar
- Kwok Y (1999) Mathematical models of financial derivatives. SpringerGoogle Scholar
- Papatheodorou B (2005) Enhanced Monte Carlo methods for pricing and hedging exotic options. University of Oxford thesisGoogle Scholar
- Wang JW, Zhang Q (2004) Pricing defaultable bond with regime switching. Contemp Math 351:361–374Google Scholar