Assignment 6 - Exotic Option Valuation using Monte Carlo simulation

A European Digital option is an option that pays a fixed amount of an asset price fixes above (in the case of a Call option) or below (in the case of a Put option).

Assume that the stock price follows Geometric Brownian Motion.

It is common to assume that:

The solution of this stochastic differential equation is

Wherezis a standard normal random variable (mean zero and standard deviation equal to one).

Build a European Digital option pricing model using by:

1)simulating future asset prices

2)determining the future option payoff

3)computing the expected value of the future option payoff

4)discounting this expected future payoff value back to the valuation date.

Your simulation model may be built in VBA, MATLAB or R (or indeed any programming language you are comfortable with).

European Digital Options are described as Binary Options in Hull's book on Options Futures and Other Derivative Securities (Section 26.10)

Monte Carlo Simulation is described in Hull's book (Section 21.6).

apply the valuation model to a three-month EUR-USD European Digital call option that pays out ?1,000,000 if EURUSD is at or above 1.2500 in three month's time.

Assume a spot rate of 1.2194, a volatility value of 5.78%, a Euro interest rate of -0.67% and a US dollar interest rate of 0.03%

31) Solver (Premium) 32) Load 33) Save 61 Deal 1 62) + 51) Pricing 53) Scenario OVML EURUSD DIVA 1.2500C 09/07/21 N1M Strategy 1 . Leg 1 . Price Date 06/07/21 17:33 Asset EURUSD Spot C Mid 1.2194 Style Digital Direction Bank sells Call/Put EUR Call Expiry 3 months 09/07/21 Delivery NY 10:00 09/09/21 Strike 1.2500 2.33% OTMF Payoff EUR 1,000,000.00 Model Black-Scholes Vol BGN C 5.774% More Market Data Points BGN Mid 21.70... Forward Mid 1.2216... EUR Depo Implied Mid -0.667...$ USD Depo USD SOFR C Mid 0.029...$ Greeks Results Price $ EUR 19.1969% R Premium EUR 191,968.56 R Margin EUR Cash 0.00