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

Sammanfattning

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 monthlyfixing dates whenever the EUR/USD spot lies inside a specified corridor, whilethe payoff is converted to GBP at maturity using a pre-specified quanto conversion.Since the payoff currency differs from the natural USD domestic currencyof the EUR/USD underlying, valuation is performed under the GBP pricing measure.Three models are compared within a common market-data framework: aquanto-adjusted at-the-money Black–Scholes benchmark, a triangle-based Dupirelocal-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 computedby Monte Carlo simulation under the GBP measure. The empirical analysis considerscorridor-width and corridor-centre sweeps for maturities of 6M, 1Y, and 3Y.The results show that the volatility smile has a material and corridor-dependenteffect on price. Narrow corridors are particularly sensitive, and the size and sign ofthe pricing difference relative to the Black–Scholes benchmark depend on both thecorridor width and the corridor location relative to the spot. The local-volatilityand multi-factor Heston models produce broadly similar prices, with differences thatare smaller than their common deviation from the benchmark. The main conclusionis that incorporating the volatility smile is important for pricing FX quanto rangeaccruals, while the choice between the two smile-consistent models is of secondaryimportance for the price level in this setting.