The Condition of the Conditionality

Author(s):  
Tumellano Sebehela

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.

Author(s):  
Puneet Pasricha ◽  
Anubha Goel

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.


2010 ◽  
Vol 13 (03) ◽  
pp. 441-458 ◽  
Author(s):  
YU-HONG LIU

After Geske (1979), compound options — options on options — have been employed in many fields in which real options are applied. The formula for a compound option is convenient to use in real project investment, but it has one drawback — the assets that underlie the compound options are usually non-tradable. This article addresses this issue and proposes two new compound option pricing formulae to overcome this drawback.


2015 ◽  
Vol 424 ◽  
pp. 194-206 ◽  
Author(s):  
Xiao-Tian Wang ◽  
Zhong-Feng Zhao ◽  
Xiao-Fen Fang

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Xinfeng Ruan ◽  
Wenli Zhu ◽  
Shuang Li ◽  
Jiexiang Huang

We study option pricing with risk-minimization criterion in an incomplete market where the dynamics of the risky underlying asset is governed by a jump diffusion equation with stochastic volatility. We obtain the Radon-Nikodym derivative for the minimal martingale measure and a partial integro-differential equation (PIDE) of European option. The finite difference method is employed to compute the European option valuation of PIDE.


2009 ◽  
Vol 13 (1) ◽  
pp. 45-73 ◽  
Author(s):  
F. Antonelli ◽  
A. Ramponi ◽  
S. Scarlatti

2007 ◽  
Vol 10 (05) ◽  
pp. 873-885 ◽  
Author(s):  
FRIEDRICH HUBALEK ◽  
CARLO SGARRA

In the present paper we give some preliminary results for option pricing and hedging in the framework of the Bates model based on quadratic risk minimization. We provide an explicit expression of the mean-variance hedging strategy in the martingale case and study the Minimal Martingale measure in the general case.


Author(s):  
Kerry E. Back

Forward measures are defined. Forward and futures contracts are explained. The spot‐forward parity formula is derived. A forward price is a martingale under the forward measure. A futures price is a martingale under a risk neutral probability. Forward prices equal futures prices when interest rates are nonrandom. The expectations hypothesis is explained. The option pricing formulas of Margabe (exchange options), Black (options on forwards), and Merton (random interest rates) are derived. Implied volatilities and local volatility models are explained. Heston’s stochastic volatility model is derived.


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