The price of a certain security follows a geometric brownian motion with drift parameter µ = 0.12 and the volatility parameter σ = 0.24.

(a) if the current price of the security is $40, find the probability that a call option, having four months until expiration and with a strike price of k = 42 will be exercised.

(b) in addition to the above information as in part (a) if the interest rate is 8%, find the risk-neutral arbitrage free valuation of the call option.

Brownian Motion- The usual model for the time-evolution of an asset price S(t) is given by the geometric Brownian motion.

Now the geometric Brownian motion is represented by the following stochastic differential equation:

To solve the problem now we have the been Data provided:

μ= 0.12,

σ=0.24,

Step-by-step explanation:

Step A:

we have, the variables of Black Scholes Model, by putting the values of variables available, we get:

Next is, "r" the risk free rate,

Step B:

We now need to calculate the parameter d₂ of the Black Scholes Model. .

Step C:

As step C is done on excel for further calculations so, do use it if you are solving it on computer.

4

step-by-step explanation:

answer: the value should be used for i in the formula of calculation the monthly payment , the interest rate per period is 0.85.

step-by-step explanation:

the given rate of interest i= 85%

in calculating the monthly payment for a loan with an interest rate compounded monthly, the value of the interest rate per period we use in the formula must be in decimal form.

to convert it in decimal, we divide it by 100, we get

hence, the value should be used for i in the formula of calculation the monthly payment , the interest rate per period is 0.85.