Three Essays On Foreign Exchange Options

Abstract

Over-the-counter (OTC) foreign exchange (FX) option market is the fourth largest derivatives market in the world. However, the extant literature on their pricing is noticeably thin, especially for less actively traded contacts, including FX options on pegged currency pairs.
To price these FX options, firstly I propose a new discrete time exponential-affine model in Chapter 3, with multiple estimation strategies and pricing confidence intervals for the resulting synthetic volatility surface. Then I test the various specifications out-of-sample on five liquid currencies versus the dollar. My specification can be estimated directly from spot FX and deposit rate quotes without recourse to quoted volatility surfaces. Results indicate that both short and long tenor OTC FX options can be accurately priced with minimal calibration.
I further extend the model to allow autoregressive conditional Poisson jumps and multiple factors in the interest rates to handle the latent interest factors in Chapter 4. I propose to adjust the discrete time-step
size to price FX options with different tenors, because this adjustment helps preserve the volatility surface dynamic of longer maturity options. In the empirical test on G7 currencies, the model is calibrated against market FX option quotes to extract the hidden factors in both
the domestic and foreign interest rates. Results show that these hidden factors have strong persistence property and certain correlation with the spot variance.
In order to price FX options on pegged FX rates, I propose to capture the trading and realignment uncertainties embedded in the forward FX rate deviation by a jump diffusion model in Chapter 5. Given the fact that transactions of FX option on such currency pairs are currently rare with very limited data available, I design a novel approach to estimate the model parameters. I then apply the proposed approach on four representative pegged currency pairs (EURDKK, USDSAR, USDQAR and USDNGN) and provide option quotes under the market convention. Distinguishing from traditional option pricing model based on historical information, the proposed model is based on forward looking information. These forward price deviation and synthetic volatility surfaces offer an alternative way to manage the FX rate risk for pegged currency pairs.