We consider the problem of option hedging in a market with proportional transaction costs. Since super-replication is very costly in such markets, we replace perfect hedging with an expected loss constraint. Asymptotic analysis for small transaction costs is used to obtain a tractable model. A general expansion theory is developed using the dynamic programming approach. Explicit formulae are ob...

We develop a new approach to valuing and hedging basket and spread options. We consider baskets of assets with potentially negative portfolio weights (spread options are a subclass of such basket options). The basket distribution is approximated using a generalized family of log-normal distributions. This approximation copes with negative basket values as well as negative skewness of the basket...

We propose a model to describe stock pinning on option expiration dates. We argue that if the open interest on a particular contract is unusually large, delta-hedging in aggregate by floor market-makers can impact the stock price and drive it to the strike price of the option. We derive a stochastic differential equation for the stock price which has a singular drift that accounts for the price...

The purpose of this paper is to investigate the use of Principal Component Analysis in finding the efficient subset of underlying assets for hedging European basket options. This asset selection technique can be used together with other hedging strategies to enhance the hedging performance. Meanwhile, it become practical and essential when some of the underlying assets are illiquid or even not ...

Understanding and measuring determinants of bid-ask spreads is decisive to clarifying the efficiency of the microstructure of any exchange and general market liquidity. This paper examines the market microstructure of a low liquidity, market maker driven option market, the relations to the underlying securities’ market and the challenges of pricing liquidity. Comparing empirical results with pr...

We consider a financial model with permanent price impact. Continuous time trading dynamics are derived as the limit of discrete rebalancing policies. We then study the problem of super-hedging a European option. Our main result is the derivation of a quasi-linear pricing equation. It holds in the sense of viscosity solutions. When it admits a smooth solution, it provides a perfect hedging stra...

We propose a new method to compute option prices based on GARCH models. In an incomplete market framework, we allow for the volatility of asset return to differ from the volatility of the pricing process and obtain adequate pricing results. We investigate the pricing performance of this approach over short and long time horizons by calibrating theoretical option prices under the Asymmetric GARC...

We propose a few variations around a simple model in order to take into account the market impact of the option seller when hedging an option. This ”retro-action” mechanism turns the linear Black and Scholes PDE into a non-linear one. This model allows also to retrieve some earlier results of [9]. Numerical simulations are then performed.