Question
The current spot price of a stock is $100 per share, and the risk-free rate is 5%. The stock pays no dividends and costs nothing
The current spot price of a stock is $100 per share, and the risk-free rate is 5%.
The stock pays no dividends and costs nothing to store.
The forward price is $105.
Each period the stock price either doubles (u=2) or halves (d=1/u=0.5)
Consider a LONG CALL position with a strike of $105 (at the money).
The system of two equations to replicate the payoff is as follows.
$95 = * $200 + B * $1.05
$ 0 = * $50 + B * $1.05
The solution to this system is.
= (95-0) / (200-50) = 95/150 = 19/30 or approximately 0.6333
B = (95 - * 200) / 1.05
= (95 19/30 * 200) / 1.05
Or -30.1587
Use and B to determine the premium on the call. Premium = $-77 . 14
In class, we derived the formula for the risk-neutral probability.
q = (1+r-d) / (u-d)
Calculate q.
q = 0 . 9 %
Show how we use risk-neutral probability (q) and the risk-free rate (r) to calculate the premium on the call and verify your answer to question 1.
The equation for the Call premium is
=Put Premium + Underlying
The call premium based on the above equation is $___ ___ . ___ ___
4. Use the risk-neutral probability and the risk-free rate to calculate the premium of a LONG PUT with a strike of $105. Show the formula and your work for full credit. 5. In class, we discussed the terminal distribution for a three-period binomial model. Use the terminal distribution to calculate the premium of a LONG CALL with a strike of $100. 4. Use the risk-neutral probability and the risk-free rate to calculate the premium of a LONG PUT with a strike of $105. Show the formula and your work for full credit. 5. In class, we discussed the terminal distribution for a three-period binomial model. Use the terminal distribution to calculate the premium of a LONG CALL with a strike of $100
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