A simple efficient approximation to price basket stock options with volatility smile

Ping Wu () and Robert J. Elliott ()
Additional contact information
Ping Wu: Nanjing University of Information Science and Technology
Robert J. Elliott: University of Calgary

Annals of Finance, 2017, vol. 13, issue 1, No 1, 29 pages

Abstract: Abstract This paper develops a new approach to obtain the price and risk sensitivities of basket options which have a volatility smile. Using this approach, the Black–Scholes model and the Stochastic Volatility Inspired model have been used to obtain an approximate analytical pricing formula for basket options with a volatility smile. It is found that our approximate formula is quite accurate by comparing it with Monte Carlo simulations. It is also proved the option value of our approach is consistent with the option value generated by Levy’s and Gentle’s approaches for typical ranges of volatility. Further, we give a theoretical proof that the option values from Levy’s and Gentle’s works are the upper bound and the lower bound, respectively, for our option value. The calibration procedure and a practical example are provided. The main advantage of our approach is that it provides accurate and easily implemented basket option prices with volatility smile and hedge parameters and avoids the need to use time-consuming numerical procedures such as Monte Carlo simulation.

Keywords: Basket options; Levy’s method; Gentle’s method; Log-normal approximation (search for similar items in EconPapers)
JEL-codes: C63 G13 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10436-017-0292-1

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