IMPORTANCE SAMPLING FOR MONTE CARLO SIMULATION TO EVALUATE COLLAR OPTIONS UNDER STOCHASTIC VOLATILITY MODEL


Finance

IMPORTANCE SAMPLING FOR MONTE CARLO SIMULATION TO EVALUATE COLLAR OPTIONS UNDER STOCHASTIC VOLATILITY MODEL

The collar option is one kind of exotic options which is useful when institutional investors wish to lock in the profit they already have on the underlying asset. Collar options can be implemented by investors on the stock they have already own. Usually investors will obtain the collar when they have enjoyed a decent gain on their investment but they want to hedge against potential downside in their shares. Collar options are very useful and practical instruments in revenue management and project management. Shan et al. (2010) study the use of collar options to manage revenue risks in real toll public-private partnership transportation projects, in particular how to redistribute the profit and losses in order to improve the effectiveness of risk management and fulfill the stakeholder’s needs. Under the constant volatility assumption, the pricing problem of collar option can be solved in the classical Black Scholes framework. However, the smile-shaped pattern of the Black Scholes implied volatilities which extracted from options has provided evidence against the constant volatility assumption in the Black Scholes model.
Jméno a příjmení autora:

Pengshi Li, Wei Li, Haidong Chen

Rok:
2020
Ročník:
23
Číslo:
2
Klíčová slova:
Importance sampling, Monte Carlo simulation, collar options, stochastic volatility
DOI (& full text):
Anotace:
The collar option is one kind of exotic options which is useful when institutional investors wish to lock in the profit they already have on the underlying asset. Under the constant volatility…více
The collar option is one kind of exotic options which is useful when institutional investors wish to lock in the profit they already have on the underlying asset. Under the constant volatility assumption, the pricing problem of collar options can be solved in the classical Black Scholes framework. However the smile-shaped pattern of the Black Scholes implied volatilities which extracted from options has provided evidence against the constant volatility assumption, so stochastic volatility model is introduced. Because of the complexity of the stochastic volatility model, a closed-form expression for the price of collar options may not be available. In such case, a suitable numerical method is needed for option pricing under stochastic volatility. Since the dimensions of state variable are usually more than two after the introduction of another volatility diffusion process, the classical finite difference method seems inefficient in the stochastic volatility scenario. For its easy and flexible computation, Monte Carlo method is suitable for evaluating option under stochastic volatility. This paper presents a variance reduction method for Monte Carlo computation to estimate collar option under stochastic volatility model. The approximated price of the collar option under fast mean reverting stochastic volatility model is derived from the partial differential equation by singular perturbation technique. The importance sampling method based on the approximation price is used to reduce the variance of the Monte Carlo simulation. Numerical experiments are carried out under the context of different mean reverting rate. Numerical experiment results demonstrate that the importance sampling Monte Carlo simulation achieves better variance reduction efficiency than the basic Monte Carlo simulation.
Sekce:
Finance

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