East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
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A PROBABILISTIC APPROACH FOR VALUING EXCHANGE OPTION WITH DEFAULT RISK

  • Kim, Geonwoo (School of Liberal Arts, Seoul National University of Science and Technology)
  • Received : 2019.12.11
  • Accepted : 2020.01.02
  • Published : 2020.01.31
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Abstract

We study a probabilistic approach for valuing an exchange option with default risk. The structural model of Klein [6] is used for modeling default risk. Under the structural model, we derive the closed-form pricing formula of the exchange option with default risk. Specifically, we provide the pricing formula of the option with the bivariate normal cumulative function via a change of measure technique and a multidimensional Girsanov's theorem.

Keywords

References

  1. F. Antonelli , A. Ramponi, S. Scarlatti, Exchange option pricing under stochastic volatility: a correlation expansion, Rev. Deriv. Res., 13(1) (2010), 45-73. https://doi.org/10.1007/s11147-009-9043-4
  2. G.H.L. Cheang, C. Chiarella, Exchange options under jump-Diffusion dynamics, Appl. Math. Financ., 18(3) (2011), 245-76. https://doi.org/10.1080/1350486X.2010.505390
  3. H. Geman, N. Karoui, J.C. Rochet, Changes of Numeraire, Changes of Probability Measure and Option Pricing, J. Appl. Probab., 32(2) (1995), 443-58. https://doi.org/10.2307/3215299
  4. G. Kim, E. Koo, Closed-form pricing formula for exchange option with credit risk, Chaos Soliton Fract., 91 (2016), 221-227. https://doi.org/10.1016/j.chaos.2016.06.005
  5. J.-H. Kim, C.R. Park, A multiscale extension of the Margrabe formula under stochastic volatility, Chaos Soliton Fract., 97 (2017), 59-65. https://doi.org/10.1016/j.chaos.2017.02.006
  6. P. Klein, Pricing Black-Scholes options with correlated credit risk, J. Bank. Financ., 50 (1996), 1211-1229. https://doi.org/10.1016/0378-4266(95)00052-6
  7. W. Margrabe, The value of an option to exchange one asset for another, J. Financ., 33(1) (1978), 177-86. https://doi.org/10.1111/j.1540-6261.1978.tb03397.x

Cited by

  1. Valuation of Exchange Option with Credit Risk in a Hybrid Model vol.8, pp.11, 2020, https://doi.org/10.3390/math8112091
  2. SIMPLIFIED APPROACH TO VALUATION OF VULNERABLE EXCHANGE OPTION UNDER A REDUCED-FORM MODEL vol.37, pp.1, 2021, https://doi.org/10.7858/eamj.2021.006