The pricing of basket-spread options
Publication in refereed journal



摘要Since the pioneering paper of Black and Scholes was published in 1973, enormous research effort has been spent on finding a multi-asset variant of their closed-form option pricing formula. In this paper, we generalize the Kirk [Managing Energy Price Risk, 1995] approximate formula for pricing a two-asset spread option to the case of a multi-asset basket-spread option. All the advantageous properties of being simple, accurate and efficient are preserved. As the final formula retains the same functional form as the Black-Scholes formula, all the basket-spread option Greeks are also derived in closed form. Numerical examples demonstrate that the pricing and hedging errors are in general less than 1% relative to the benchmark results obtained by numerical integration or Monte Carlo simulation with 10 million paths. An implicit correction method is further applied to reduce the pricing errors by factors of up to 100. The correction is governed by an unknown parameter, whose optimal value is found by solving a non-linear equation. Owing to its simplicity, the computing time for simultaneous pricing and hedging of basket-spread option with 10 underlying assets or less is kept below 1 ms. When compared against the existing approximation methods, the proposed basket-spread option formula coupled with the implicit correction turns out to be one of the most robust and accurate methods.
著者Lau CS, Lo CF
期刊名稱Quantitative Finance
出版社Taylor & Francis (Routledge): SSH Titles
頁次1971 - 1982
關鍵詞Black-Scholes model; Closed-form approximation; Derivatives pricing; Multi-variate contingent; Parametric correction; Portfolio hedging
Web of Science 學科類別Business & Economics; Business, Finance; Economics; Mathematical Methods In Social Sciences; Mathematics; Mathematics, Interdisciplinary Applications; Social Sciences, Mathematical Methods

上次更新時間 2020-01-08 於 02:38