Consider a European call option on a non$-$dividend$-$paying stock where

the stock price is

$$40,$ the strike price is $$40,$ the risk$-$free rate is $4\%$ per annum, the

volatility is $30\%$ per

annum, and the time to maturity is $6$ months.

$($a$)$ Calculate $u,d($f$$rmula de Ross$),$ and $p$ for a two$-$step tree.

$($b$)$ Value the option using a two$-$step tree.

$($c$)$ Verify that DerivaGem gives the same answer.

$($d$)$ Use DerivaGem to value the option with $5,50,100,$ and $500$ time

steps.

u

d

p

Valuaci$$n con $5$ Steps, $50,100$ and $500$ time steps