Tests of an American Option Pricing Model on the Foreign Currency Options Market

Exchange-traded currency options are a recent innovation in the Indian financial market and their pricing is as yet unexplored. The objective of this research paper is to empirically compare the pricing performance of two well-known option pricing models – the Black-Scholes-Merton Option Pricing Model (BSM) and Duan’s NGARCH option pricing model – for pricing exchange-traded currency options on the US dollar-Indian rupee during a recent turbulent period. The BSM is known to systematically misprice options on the same underlying asset but with different strike prices and maturities resulting in the phenomenon of the ‘volatility smile’. This bias of the BSM results from its assumption of a constant volatility over the option’s life. The NGARCH option pricing model developed by Duan is an attempt to incorporate time-varying volatility in pricing options. It is a deterministic volatility model which has no closed-form solution and therefore requires numerical techniques for evaluation. In this paper we have compared the pricing performance and examined the pricing bias of both models during a recent period of volatility in the Indian foreign exchange market. Contrary to our expectations the pricing performance of the more sophisticated NGARCH pricing model is inferior to that of the relatively simple BSM model. However orthogonality tests demonstrate that the NGARCH model is free of the strike price and maturity biases associated with the BSM. We conclude that the deterministic BSM does a better job of pricing options than the more advanced time-varying volatility model based on GARCH.

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Ensuring More Is Better: On the Simultaneous Application of Stock and Options Data to Estimate the GARCH Options Pricing Model

The Journal of Derivatives ◽

10.3905/jod.2018.1.067 ◽

2018 ◽

Keyword(s):

Option Pricing ◽

Stock Prices ◽

Options Pricing ◽

Asymptotic Result ◽

Option Prices ◽

Options Market ◽

Pricing Model ◽

Simultaneous Application ◽

Option Values ◽

Option Pricing Model

The most common approach in fitting option pricing models to market data is first to make an assumption about the underlying asset’s returns process and then develop an option pricing model for that process that is tested against market option prices. The returns process is estimated from historical data, option values are computed, and then compared against a cross-section of prices from the options market. Unfortunately, this often does not work well, and plainly it is inefficient in its use of the data. However, efforts to combine returns data from the asset market and prices from the options market into a single estimation have also not had much success. In this article, Chang, Cheng, and Fuh propose a new procedure to combine data from both markets in the estimation, in which options are assumed to be subject to random pricing noise relative to model values. The additional slack gives the estimator better ability to match prices in both markets. The article contrasts the performance of the full model approach with an approach that only uses stock prices or options prices to fit an option pricing model based on an underlying GARCH process. The value of the combined approach is demonstrated both theoretically as an asymptotic result in the model and also in a Monte Carlo simulation.

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