Question $5(25$ points$)$

Consider a put option in a stock with $1$ year to maturity. The strike price is SEK $85,$ the

relevant risk$-$free rate of interest is $3$ percent on an annual basis, and the current stock price

is SEK $80.$ Assume that the stock price at the end of the year is either SEK $70$ or SEK $90.$

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 put

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 put option. $(4$p$)$

d$)$ Consider a call 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 call option? $(7$p$)$

e$)$ Suppose you currently hold $345$ of the underlying stock. Explain what position and

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