Problem $22-1$ One$-$step binomial model

Over the coming year, Ragwort's stock price will halve to $$60$ from its current level of $$120$ or it will rise to $$240.$ The one$-$year interest

rate is $10\%.$

a$.$ What is the delta of a one$-$year call option on Ragwort stock with an exercise price of $$120?$

Note: Round your answer to $4$ decimal places.

b$.$ What is the amount of the loan in the replicating portfolio?

Note: Do not round intermediate calculations. Round your answer to $2$ decimal places.

c$.$ Given the delta computed in part $($a$),$ how much would be borrowed if the replicating$-$portfolio method was used to value the call

option?

Note: Do not round intermediate calculations. Round your answer to $2$ decimal places.

d$.$ In a risk$-$neutral world, what is the probability that Ragwort stock will rise in price?

Note: Round your answer to $2$ decimal places.

e$.$ Using the risk$-$neutral method, what is the value of the call option?

Note: Do not round intermediate calculations. Round your answer to $2$ decimal places.

f$.$ If someone told you that in reality there is a $60\%$ chance that Ragwort's stock price will rise to $$240,$ would you change your view

about the value of the option?