We explore the robust replication of forward-start straddles given quoted (Call and Put options) market data. One approach to this problem classically follows semi-infinite linear programming arguments, and we propose a discretisation scheme to reduce its dimensionality and hence its complexity....

We provide a full characterisation of the large-maturity forward implied volatility smile in the Heston model. Although the leading decay is provided by a fairly classical large deviations behaviour, the algebraic expansion providing the higher-order terms highly depends on the parameters, and...

Classical (Ito diffusions) stochastic volatility models are not able to capture the steepness of small-maturity implied volatility smiles. Jumps, in particular exponential Levy and affine models, which exhibit small-maturity exploding smiles, have historically been proposed to remedy this (see...

In this paper we investigate the asymptotics of forward-start options and the forward implied volatility smile in the Heston model as the maturity approaches zero. We prove that the forward smile for out-of-the-money options explodes and compute a closed-form high-order expansion detailing the...

We prove here a general closed-form expansion formula for forward-start options and the forward implied volatility smile in a large class of models, including the Heston stochastic volatility and time-changed exponential Levy models.This expansion applies to both small and large maturities and...

We introduce a stacking version of the Monte Carlo algorithm in the context of option pricing. Introduced recently for aeronautic computations, this simple technique, in the spirit of current machine learning ideas, learns control variates by approximating Monte Carlo draws with some specified...

We rigorize the work of Lewis (2007) and Durrleman (2005) on the small-time asymptotic behavior of the implied volatility under the Heston stochastic volatility model (Theorem 2.1). We apply the Gärtner-Ellis theorem from large deviations theory to the exponential affine closed-form expression...

We build on of the work of Henry-Labordµere and Lewis on the small-time behaviour of the return distribution under a general local-stochastic volatility model with zero correlation. We do this using the Freidlin-Wentzell theory of large deviations for stochastic differential equations, and then...

Using the Gartner-Ellis theorem from large deviation theory, we characterize the leading-order behaviour of call option prices under the Heston model, in a new regime where the maturity is large and the log-moneyness is also proportional to the maturity. Using this result, we then derive the...

We show that if the discounted Stock price process is a continuous martingale, then there is a simple relationship linking the variance of the terminal Stock price and the variance of its arithmetic average. We use this to establish a model-independent upper bound for the price of a continuously...