Conditional-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.

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VALUATION OF EXCHANGEABLE CONVERTIBLE BONDS

International Journal of Theoretical and Applied Finance ◽

10.1142/s0219024904002657 ◽

2004 ◽

Vol 07 (06) ◽

pp. 701-721 ◽

Cited By ~ 1

Author(s):

MARCO REALDON

Keyword(s):

Finite Difference ◽

Finite Difference Method ◽

Difference Method ◽

Financial Distress ◽

Convertible Bonds ◽

Valuation Model ◽

Exchange Option

This paper provides a structural valuation model for exchangeable convertible bonds, since such bonds are widespread by now. The model is solved through the Hopscotch finite difference method. As the issuer owns the underlying shares, exchangeable convertibles may be called and the exchange option may be exercised even as the issuer experiences financial distress. The value of exchangeable convertibles always decreases in the volatility of the issuer's assets (unlike the value of ordinary convertibles) and decreases in the correlation between the underlying shares and the issuer's assets. The analysis confirms that the dominant motive for issuing exchangeable convertibles is likely to be to dispose of the underlying shares.

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On the option valuation and decomposition of exchange option

Korean Journal of Computational & Applied Mathematics ◽

10.1007/bf03021563 ◽

2002 ◽

Vol 9 (2) ◽

pp. 575-581

Author(s):

Won Choi ◽

Seung Chul Ahn

Keyword(s):

Option Valuation ◽

Exchange Option

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The Condition of the Conditionality

Review of Pacific Basin Financial Markets and Policies ◽

10.1142/s0219091521500272 ◽

2021 ◽

Author(s):

Tumellano Sebehela

Keyword(s):

Probability Theory ◽

Option Pricing ◽

Simultaneous Occurrence ◽

Option Value ◽

Hedging Strategy ◽

Compound Options ◽

Exotic Option ◽

Exchange Options ◽

Nikodym Derivative ◽

Exchange Option

The interdependence of options is common among compound options. Moreover, this interconnectedness is synonymous with probability theory-how a set of axioms are treated. The conditionality, where one option value is dependent on another option, has spilled over to option pricing, especially exchange options. However, it seems that no study has explored whether that simultaneous occurrence of two options is conditional or not. This study uses conditional approaches (Radon–Nikodým derivative and probability theory) to illustrate conditionality in an exchange option. Furthermore, hedging strategy is derived based on straddles. The results show that due to conditionality another exotic option, tri-conditional option (also known as triple option) is derived. The hedging of a triple option encompasses both dynamic and static techniques.

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