Question $4(20$ points$)$ d$)$ Consider a put option in the same stock as above, with the same characteristics $($i$.$e$.$

time to maturity, risk$-$free rate of interest, strike and stock price, and potential

prices at the end of the year$).$ Using the Put$-$call parity condition, what is the price

of the put option? $(7$p$)$

e$)$ Suppose you currently hold $275$ of the underlying stock. Explain what position and

how many call options that are needed to create a delta$-$neutral portfolio? $(4$p$)$

a$)$ On the market the price for a stock is SEK $175.$ The stock pays an annual dividend

of SEK $5.$ The risk$-$free interest rate is $2\mathrm{.}25\%$ and the futures price for the stock, with

maturity in one year, is $180.($i$)$ Calculate the dividend yield for the stock; $($ii$)$ Show,

given these prices, that there is an arbitrage opportunity and the profit from

exploiting this opportunity $(10$p$)$

b$)$ What relationship do you theoretically expect between the futures price and

expected spot price $($e$.$g$.$ the spot price prevailing in one year$)$ for gold, assuming

the beta for gold is $-0\mathrm{.}2?$ Explain in detail with words and illustrate in a figure. $(10$p$)$

Question $5(25$ points$)$

Consider a call option in a stock with $1$ year to maturity. The strike price is SEK $60,$ the

relevant risk$-$free rate of interest is $2$ percent on an annual basis, and the current stock price

is SEK $65.$ Assume that the stock price at the end of the year is either SEK $40$ or SEK $80.$

a$)$ Explain shortly in words what is meant by the hedge ratio. Calculate the hedge ratio

given the above information. $(2$p$)$

b$)$ Using the binomial pricing model $($two$-$state model$),$ what is the price of the call

option? Show and explain your calculations $(8$p$)$

c$)$ Explain what is meant by the intrinsic and time value of an option. Calculate the

intrinsic and time value for the above call option. $(4$p$)$