We consider option hedging and pricing for a large agent. The large agent affects the market’s demand-supply equilibrium and, therefore, the market prices of financial instruments. By assuming a specific large agent’s effect function for the underlying asset we derive the corresponding effect function for call options on that asset. As we show, the price of a call option in our model is the sol...

This paper analyzes corporate bond valuation and optimal call and default rules when interest rates and firm value are stochastic. It then uses the results to explain the dynamics of hedging. Bankruptcy rules are important determinants of corporate bond sensitivity to interest rates and firm value. Although endogenous and exogenous bankruptcy models can be calibrated to produce the same prices,...

This paper introduces a dual way to price American options, based on simulating the paths of the option payoff, and of a judiciously chosen Lagrangian martingale. Taking the pathwise maximum of the payoff less the martingale provides an upper bound for the price of the option, and this bound is sharp for the optimal choice of Lagrangian martingale. As a first exploration of this method, four ex...

Consider the performance of an options writer who mis-speciies the dynamics of the price process of the underlying asset by overestimating asset price volatility. When does he overprice the option? If he follows the hedging strategy suggested by his model, when does the terminal value of his strategy dominate the option payout? We show that both these events happen if the option payoo is a conv...

The QLBS model is a discrete-time option hedging and pricing model that is based on Dynamic Programming (DP) and Reinforcement Learning (RL). It combines the famous Q-Learning method for RL with the Black-Scholes (-Merton) model’s idea of reducing the problem of option pricing and hedging to the problem of optimal rebalancing of a dynamic replicating portfolio for the option, which is made of a...

The pricing problem of lookback option with a fixed proportion of transaction costs is investigated when the underlying asset price follows a fractional Brownian motion process. Firstly, using Leland's hedging method a partial differential equation satisfied by the value of the lookback option is derived. Then we obtain its numerical solution by constructing a Crank-Nicolson format. Finally, th...