Question

The following numbers were randomly generated from a standard normal distribution: -0.25 , 0.3 , 1.5 , -1.2, -1.65, 1.5 1) Given interest rate = 0.01 and volatility parameter = 0.2, compute the drift parameter of a security following a risk-neutral geometric Brownian motion. 2). Suppose security ABC follows a geometric Brownian motion with the parameters given in 1). If the initial closing price of ABC S0 = S = 50, compute 6 more simulated daily closing prices for ABC. 3). If the strike price of a European call is = 52, and the expiration of this call is at the end of 6 days, what is the payoff of the call? That is, what is the value of (S6 ?K )+?

Answer 1

1)solution:

given data:

s = 50

= 0.01

= 0.2

assuming t is for 1 week so t value is

t = 0.0192

as per brownian process,

the formula of  S/S = *t+*(root(t))

susbstitute the all values in above quation

S/50 = 0.01*0.0192+0.2**(root(0.0192))

S	50
	0.01
	0.2
t	0.0192
standard normal distributions are	-0.25	0.3	-1.2	-1.65	1.5
S	-0.33681	0.425292	-1.65317	-2.27671	2.088061

2) Stock price over a week as shown in below:

day	initial stock price	change in stock price	closing stock price
1	50	-.0336810162	49.66318984
2	49.66318984	0.425292194	50.08848203
3	50.08848203	-1.653168775	48.43531326
4	48.43531326	-2.276707066	46.15860619
5	46.15860619	2.088060969	48.24666716
6	48.24666716	0	48.24666716

3)

stock price	share price	pay off
52	50	0