Question #$2$: Option Valuation $[28$ Points$]$

Use the following scenario to answer Parts $($a$)($b$)$

Suppose that the price of a share of Stryker Corp $($SYK$)$ today is at $$340.$ You have forecasted that in one

year the stock price will either rise to $$376$ or fall to $$316.$

Suppose further that you can either buy or sell a call option on SYK stock with a strike price of $$337$

Assume that this is a European style contract that expires exactly in one year and that the risk$-$free interest

rate is $5\mathrm{.}5\%.$

$($a$)$ Refer to Scenario $3.$ Calculate the Hedge Ratio $($H$).[4$ Points$]$

$($b$)$ Refer to the above scenario. Use the Binominal Option Pricing Model to calculate the price of the

SYK call option with a strike price of $$337$ today. $[10$ Points$]$

Use the following scenario to answer Parts $($c$)($d$)$

Consider a share of On Holding AG stock $($ONON$)$ that currently trades for $$33\mathrm{.}23.$ A call option on this

stock has a strike price of $$31$ and it expires in $9$ months $(0\mathrm{.}75$ years$).$ Assume that the standard deviation

$(\backslash$sigma $)$ for the stock is $0\mathrm{.}45,$ the risk$-$free rate $($r$)$ is $0\mathrm{.}05,$ and the dividend rate $(\backslash$delta $)$ is $0.$

$($c$)$ Calculate the intrinsic value of the call option of ONON using the Black$-$Scholes option pricing

formula. $[$Hint: You will need to use a standard normal distribution table. Also when calculating d$1$

and d$2$ round to two decimal places.$][11$ Points$]$

$($d$)$ Using your answer from Part $($c$)$ what is the price of the put$-$option, with the same strike price and

expiration date as the call, using the same information? $[3$ Points$]$