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Josephidou, Frederick (2021) An Alternative FX Option Pricing Model: A Discrete Mixture of Normal Distributions. PhD thesis. SOAS University of London. DOI: https://doi.org/10.25501/SOAS.00038362

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Abstract

With the introduction of the Black and Scholes (1973) and R. C. Merton (1973) (BSM) option pricing model, researchers and practitioners have been continually looking to amend and extend the model to improve performance. This thesis will take an alternative approach to addressing the limitations of the BSM model. Rather than append an extension to the model by relaxing one or more of the assumptions: R. C. Merton (1976), Derman and Kani (1994), Bakshi, Cao, and Chen (1997) and Dumas, Fleming, and Whaley (1998), this thesis applied a suitable transformation to the data to elicit more information relating to its distribution to ensure compliance with the BSM assumption of normality. The aim is to identify the three stages that make up the foreign exchange (FX) option price, namely: i. Defining the constituent elements that explain the FX spot price to model the FX market behaviour. This thesis shows that the FX market can be represented by a system of attributes: order bid-ask spread and triangulation. These attributes, although transmit information unique to their own function; also operate as a system to arrive at the quoted price. These elements will be used to remodel the FX market behaviour in describing it as a stochastic price process. ii. Represent the FX market behaviour by an appropriate stochastic price process. The stochastic FX price process, characterised by the system of attributes describing the FX market, defines the fundamental equation, adhering to the assumption of normality, to explain the FX option pricing formula. The Kon (1984) discrete mixture of normal distributions model was utilised in describing the market systemic function to arrive at the stochastic FX price process. iii. Applying the BSM method to the fundamental equation proposed by the thesis afforded an alternative FX option price model. The collective affect of each attribute results in a skewed, leptokurtic distribution for the price returns. The thesis demonstrates that the constituent pricing elements are normally distributed and affect the price distribution by a proportionate shift parameter. The modified stochastic process is the basis of the fundamental equation that is applied to the BSM methodology to arrive at an alternative, modified closed form FX option pricing model. Under the presumption that the more exact the option pricing model the more accurate the forecasting ability, the forecasting performance of each model was compared utilising risk reversal options. Forecasting the movement in the FX spot market, the precision of the modified FX option pricing formula was compared to the market leading BSM pricing model. Hence, accepting the evaluation criterion as an indicator of the senior option pricing model, the result for the alternative FX option pricing formula were very promising. The thesis clearly demonstrates that the modified option pricing model outperforms the BSM model using trend reversal indicators but is not so definite with the directional trend indicators. The encouraging initial results con rm the necessity for this research and present opportunities for further study, namely, i. What is the true number of N normal distributions in the Kon (1984) model? This will directly impact the size of the variance shift parameter in the fundamental equations. ii. What pricing information is contained in an option that can be used to forecast price movements? Intuitively options contain information about forward pricing, thus interpreting this information is central to any potential trading strategies. iii. What is the appropriate trading strategy to extract forward pricing information contained in an option offering a profitable opportunity?

Item Type: Theses (PhD)
SOAS Departments & Centres: SOAS Research Theses
Supervisors Name: Pasquale Scaramozzino and Hong Bo
DOI (Digital Object Identifier): https://doi.org/10.25501/SOAS.00038362
Date Deposited: 30 Nov 2022 15:47
URI: https://eprints.soas.ac.uk/id/eprint/38362

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