Quantity Adjusted Option Pricing: An Investigation

We explored quantity adjusted option (quanto) pricing theory in this Senior Project. Quantos are vanilla equity options with a foreign exchange (FX) component, offering an investor the right but not the obligation to exercise an investment in a foreign company with a payout in the investor’s domestic currency. We looked at five currency pairs (USD-GBP, USD-AUD, GBP-EUR, AUD-JPY, and USD-MXN), all of which have volatile FX rates. For each currency pair, we gathered data for the five largest companies in the foreign market (by market capitalization). To narrow our scope on call quantos we focused on four strike choices (5, 10, 15, and 20% above the current stock price) and four maturities (0.5, 1, 2, and 5 years). We then removed all observations containing missing data, calculated a 31-day stock-FX correlation, determined a modified underlying stock price, and found a final quanto price for each strike-maturity combination using the Black-Scholes option pricing formula. After cleaning the data, we regressed the quanto price on the following variables: stock price, dividend yield, volatility of the underlying stock, volatility of the FX rate, FX rate, domestic risk free rate, foreign risk free rate, stock-FX correlation, and the interaction between the two riskfree rates. We found that fewer variables became statistically relevant as the maturity lengthened, though the dividend yield, volatility of the underlying stock, volatility of the FX rate, and stock-FX correlation persist to be important in quanto pricing. Moreover, the R² values decreased as maturity increased for all four strike choices. For the 25 companies, the maximum R² value was 40.7% for a maturity of 0.5 years for LVMH (LVMUY), meaning 40.7% of the variability in the quanto price can be explained by the input variables. This is a promising value which offers potential for future work to delve deeper into LVMH and/or European-based companies and possible arbitrage opportunities.