# Asian option control variate matlab

Now by the risk-neutral valuation formula, we have On the one hand, we have where we used the fact that follows standard normal distribution and On the other hand, we got By change of variable we have Now putting all pieces together, we have Now we are ready to compute. Asian Geometric Asian option control variate matlab as a Control Variate The payoff of Asian geometric option is given by Under the classical Black-Scholes model, we know that the underlying asset is a geometric Brownian motion given by see Bjork [ 12 ] for more details Proposition 1. Indeed, we have Asian option control variate matlab that the integral is normal with mean 0 and variance To simplify our notation, we denote.

Now by the risk-neutral valuation formula, we have On the one hand, we have where we used the fact that follows standard normal distribution and On the other hand, we got By change of variable we have Now putting all pieces together, we have Now we are ready to asian option control variate matlab. By chain rule, we have 5. Note that the primary purpose of the code presented here is to show how to implement the control variates technique and to price asian option control variate matlab option. In this paper, we study the Greeks of Asian arithmetic call option.

Many authors are devoted to the numerical approximation of the close form formula see Turnbull and Wakeman [ 2 ], Vorst [ 3 ], Levy [ 4 ], and Levy and Turnbull [ 5 ]. Step 2 approximating the payoff functions of both Asian arithmetic and Asian geometric asian option control variate matlab. Once the approximated pricing formula for the Asian arithmetic option is available, one can obtain the Greeks by applying a shock on the underlying asset price with the finite difference methods. Asian options have appealing features that attract many investors.

Indeed, Next, we simulate copies of the Asian arithmetic option payoff Similarly, we simulate copies of the Asian geometric option payoff. The payoff of Asian arithmetic average call option with strike price is given by Since no analytical solution is known, asian option control variate matlab variety of numerical approximation techniques have been developed to analyze the Asian arithmetic average option. Next, we briefly introduce some classical variance reduction techniques. It would reduce the standard error ofeven with a moderate size of.

The most effective variance reduction technique is the control variate method. Our method provides an efficient solution to the hedging strategy with Asian options. Also, in [ 15 ], a PDE approach was utilized to understand the numerical value of the Asian option Greeks. We also asian option control variate matlab that, in recent years, many authors have been actively involved in the research of calculating Greeks of Asian type option using various approaches.

We denoteand then we generate sample paths and by the following iterative steps: Let us first fix some parameters: Now by the risk-neutral valuation formula, asian option control variate matlab have On the one hand, we have where we used the fact that follows standard normal distribution and On the other hand, we got By change of variable we have Now putting all pieces together, we have Now we are ready to compute. It would reduce the standard error ofeven with a moderate size of.