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Pricing of Digital Option by Monte Carlo Method with Adaptive Scheme
CQF Institute Talk

Wednesday, 29 May London and online 

Discontinuities in the payoff function can cause inaccuracies and instabilities for numerical method when pricing financial contract. Here, we specialize in the valuation of digital options by discretizing the Stochastic Differential Equation (SDE) for the asset price and by Monte Carlo simulations. We consider a Single Refinement Monte Carlo (SRMC) which can be built for any non-adaptive discrete time numerical method. It consists to refine only simulated paths that lands close to the contractual strike price where a small discretisation discrepancy w.r.t to true spot price can generate large payoff error. Our numerical analysis provides estimates for the weak, strong errors and the expected computational complexity of the SRMC scheme. It is also complemented by numerical experiments in two well-known skew/smile: time homogeneous hyperbolic local volatility and correlate exponential Ornstein-Uhlenbeck (expOU) stochastic volatility models where we show that the SRMC scheme can be combined with standard variance reduction methods to achieve better convergence.

This talk will discuss:

-An introduction to pricing of Digital Option
-Single refinement Monte Carlo scheme for Digital Options
-Numerical experiments
-Conclusions and Discussions

Speaker Bio 
Julien Hok is a quantitative analyst at CA-CIB, London. He was previously a quantitative analyst in equity at Santander for 6 years and worked in interest rates at Citi Group. Julien holds a PhD in Financial Mathematics from Ecole Polytechnique, France. His research is in perturbation methods to obtain approximation pricing formulas for exotic and hybrid products in equity/ FX / interest rates, option pricing by polynomial expansion of density function and calibration of local volatility model with stochastic rates by PDE approach.


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