Question

Consider a spread call option that has pay-off (ST​−VT​−K)+ where St​=S0​exp((r−σ12​/2)t+σ1​Wt​)Vt​=V0​exp((r−σ22​/2)t+σ2​Bt​)​ and [Wt​,Bt​] is a vector-valued Brownian motion with co-variance matrix Σ=[2.25​.251​] Implement the Monte Carlo method for this with n=5000,n=10,000 samplesnd with data S0​=50,V0​=45,r=0.05,σ1​=0.25,σ2​=0.3,K=5,T=1. Write the approximate value of the call option along with the standard error.

Answer 1

The student's question is about valuing a spread call option with the Monte Carlo simulation method using given financial data and parameters.

Step-by-step explanation:

The student is asking about the valuation of a spread call option using a Monte Carlo method with specific financial parameters given. To approximate the value of this call option, one would simulate the underlying asset price paths for St and Vt using geometric Brownian motion as described, correlating them according to the covariance matrix Σ. For each sample path, the pay-off (ST - VT - K)+ is calculated. Then, the mean of these pay-offs is discounted back to present value using the risk-free rate r. This process is repeated for 5000 and then 10,000 sample paths to estimate the option's value and standard error.