A Delayed Black and Scholes Formula I

2006/04/28 by Mercedes Arriojas, Yaozhong Hu, Arriojas, Mercedes +5 · 5 citations
Economics, Econometrics and Finance · Mathematics · #FOS: Economics and business #FOS: Mathematics #Pricing of Securities (q-fin.PR) #Probability (math.PR) #Statistics Theory (math.ST) #math.PR #math.ST #q-fin.PR #stat.TH

paper · pdf · doi:10.48550/arxiv.math/0604640

arxiv created 2006/04/28 · arxiv updated 2009/12/01

Abstract

In this article we develop an explicit formula for pricing European options when the underlying stock price follows a non-linear stochastic differential delay equation (sdde). We believe that the proposed model is sufficiently flexible to fit real market data, and is yet simple enough to allow for a closed-form representation of the option price. Furthermore, the model maintains the no-arbitrage property and the completeness of the market. The derivation of the option-pricing formula is based on an equivalent martingale measure.

Cited by

• Stochastic Maximum Principle for Optimal Control of Anticipated Backward Stochastic Systems with Delays
• Linear-Quadratic Non-zero Sum Differential Game with Asymmetric Delayed Information
• Convergence in probability of numerical solutions of a highly non-linear delayed stochastic interest rate model
• Strong convergence in the infinite horizon of numerical methods for stochastic delay differential equations
• Implicit numerical approximation for stochastic delay differential equations with the nonlinear diffusion term in the infinite horizon

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