Closed-form pricing formula for exchange option with credit risk

2016 ◽  
Vol 91 ◽  
pp. 221-227 ◽  
Author(s):  
Geonwoo Kim ◽  
Eunho Koo
Keyword(s):  
Credit Risk ◽  
Closed Form ◽  
Pricing Formula ◽  
Exchange Option

A CLOSED-FORM PRICING FORMULA FOR EUROPEAN EXCHANGE OPTIONS WITH STOCHASTIC VOLATILITY

2021 ◽  
pp. 1-10
Author(s):  
Puneet Pasricha ◽  
Anubha Goel
Keyword(s):  
Closed Form ◽  
Stochastic Volatility ◽  
Closed Form Solution ◽  
Form Solution ◽  
Stochastic Volatility Model ◽  
Strike Price ◽  
Volatility Model ◽  
Exchange Options ◽  
Pricing Formula ◽  
Exchange Option

This article derives a closed-form pricing formula for the European exchange option in a stochastic volatility framework. Firstly, with the Feynman–Kac theorem's application, we obtain a relation between the price of the European exchange option and a European vanilla call option with unit strike price under a doubly stochastic volatility model. Then, we obtain the closed-form solution for the vanilla option using the characteristic function. A key distinguishing feature of the proposed simplified approach is that it does not require a change of numeraire in contrast with the usual methods to price exchange options. Finally, through numerical experiments, the accuracy of the newly derived formula is verified by comparing with the results obtained using Monte Carlo simulations.

scholarly journals Closed-form pricing formula for foreign equity option with credit risk

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Donghyun Kim ◽  
Ji-Hun Yoon ◽  
Geonwoo Kim
Keyword(s):  
Credit Risk ◽  
Closed Form ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Transform Method ◽  
Equity Options ◽  
Over The Counter ◽  
3 Dimensional ◽  
Numerical Result ◽  
Pricing Formula

AbstractSince credit risk in the over-the-counter (OTC) market has undoubtedly become very important issue, credit risk has to be considered when the options in the OTC market are priced. In this paper, we consider the valuation of foreign equity options with credit risk. In order to derive a closed-form pricing formula of this option, we adopt the partial differential equation (PDE) approach and use the Mellin transform method to solve the PDE. Specifically, triple Mellin transforms are used, and the pricing formula is presented as 3-dimensional normal cumulative distribution functions. Finally, we verify that our closed-form formula is accurate by comparing it with the numerical result from the Monte-Carlo simulation.

scholarly journals Pricing the Zero-Coupon Bond and its Fair Premium Under a Structural Credit Risk Model with Jumps

2011 ◽  
Vol 48 (02) ◽  
pp. 404-419 ◽  
Author(s):  
Yinghui Dong ◽  
Guojing Wang ◽  
Rong Wu
Keyword(s):  
Laplace Transform ◽  
Credit Risk ◽  
Closed Form ◽  
Risk Model ◽  
Market Value ◽  
Credit Spread ◽  
The Laplace Transform ◽  
Credit Risk Model ◽  
Coupon Bond ◽  
Fair Premium

In this paper we consider a structural form credit risk model with jumps. We investigate the credit spread, the price, and the fair premium of the zero-coupon bond for the proposed model. The price and the fair premium of the bond are associated with the Laplace transform of default time and the firm's expected present market value at default. We give sufficient conditions under which the Laplace transform and the expected present market value of a firm at default are twice continuously differentiable. We derive closed-form expressions for them when the jumps have a hyperexponential distribution. Using the closed-form expressions, we obtain numerical solutions for the default probability, the credit spread, and the fair premium of the bond.

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