Question
Question 1 Consider the derivation of the Black-Scholes model of option pricing. Let S=S(t) be the underlying stock price at time t and let f=f(S,
Question 1 Consider the derivation of the Black-Scholes model of option pricing. Let S=S(t) be the underlying stock price at time t and let f=f(S, t) be the option price at time t.
a) Write down the value P of the portfolio defined in the Black-Scholes model. [2 marks]
b) Use Its lemma to find an expression for the change f in the discrete time t. [5 marks]
c) Use the expression you have found in point b) to find an expression for the discrete change in the value of the Black-Scholes portfolio. [5 marks]
d) Find the number of shares Delta so that the random component is eliminated from the discrete change in the value of the Black-Scholes portfolio? [3 marks]
e) Given the choice you indicated for the Black-Scholes Delta, now derive the BlackScholes partial differential equation. [15 marks]
Step by Step Solution
There are 3 Steps involved in it
Step: 1
Get Instant Access to Expert-Tailored Solutions
See step-by-step solutions with expert insights and AI powered tools for academic success
Step: 2
Step: 3
Ace Your Homework with AI
Get the answers you need in no time with our AI-driven, step-by-step assistance
Get Started