Pricing FX Quanto Range Accruals: A Comparative Study of Pricing Models

Abstract

This thesis investigates the impact of volatility modelling on the valuation of a EUR/ USD range accrual quantoed to GBP. The product accrues coupon at monthly fixing dates whenever the EUR/USD spot lies inside a specified corridor, while the payoff is converted to GBP at maturity using a pre-specified quanto conversion. Since the payoff currency differs from the natural USD domestic currency of the EUR/USD underlying, valuation is performed under the GBP pricing measure. Three models are compared within a common market-data framework: a quanto-adjusted at-the-money Black–Scholes benchmark, a triangle-based Dupire local-volatility model, and the multi-factor FX Heston model of De Col, Gnoatto, and Grasselli. The local-volatility and Heston models are calibrated to EUR/USD, GBP/USD, and EUR/GBP implied-volatility smiles, and their prices are computed by Monte Carlo simulation under the GBP measure. The empirical analysis considers corridor-width and corridor-centre sweeps for maturities of 6M, 1Y, and 3Y. The results show that the volatility smile has a material and corridor-dependent effect on price. Narrow corridors are particularly sensitive, and the size and sign of the pricing difference relative to the Black–Scholes benchmark depend on both the corridor width and the corridor location relative to the spot. The local-volatility and multi-factor Heston models produce broadly similar prices, with differences that are smaller than their common deviation from the benchmark. The main conclusion is that incorporating the volatility smile is important for pricing FX quanto range accruals, while the choice between the two smile-consistent models is of secondary importance for the price level in this setting.