I presented a paper at the IAFA conference in UCC during the Easter break of 2011. Spread Options can be used as a hedge for stat arb trading. I'm hoping to do a little bit of research on stat arb next.
A Comparison of Pricing Methods for Spread Options
This paper is a numerical comparison of Monte Carlo, Kirk's, Deng, Li and Zhou's (DLZ), Margrabe's and Haug's methods for pricing European spread options. It then compares these methods with simulated option prices using data from the FTSE 100, FTSE All Share, Dow Jones and Nasdaq.
The five methods under consideration were in close agreement for exchange options, and for long expiry spread options. For all methods there was closer agreement for high positive correlations, and for shorter expiries. The methods in sequence of increasing size are Haug < DLZ ~ Kirk < Monte Carlo, and for exchange options Haug < Margrabe < Monte Carlo.
The simulated prices were higher than the other methods, the ratio was reasonably constant for longer than one day expiries.
Kirk's method was the most useful in this examination; it is preferable to DLZ as it does not involve as many calculations of the inverse cumulative normal distribution.
The Irish Accounting and Finance Association's website:
The Spread Options paper:
Brandimarte,P. (2006) Numerical Methods in Fianance and Economics, 2nd ed. New Jersey, Wiley and Sons, Inc.
Carmona, R. and Durrleman, V. (2003) ‘Pricing and Hedging Spread Options’, Society for Industrial and Applied Mathematics Review, 45(4), 627–685.
Deng, S.J., Li, M. and Zhou, J. (2008) [online], ‘Closed-form Approximations for Spread Option Prices and Greeks’, available: http://mpra.ub.uni-muenchen.de/6994/ MPRA Working Paper No. 6994.
Haug, E.G. (2007) The Complete Guide to Option Pricing Formulas, 2nd ed., New York: Mc Graw Hill, pp 213 – 215.
Margrabe, W. (1978) The Value of an Option to Exchange One Asset for Another, The Journal of Finance, 33 (1) 177-186