### The effective risk-free rate of interest

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An asset has a current price of Rs 40. Over the next year, the price will either increase to Rs 48 with probability p, or decrease to Rs 38 with probability (1-p). The effective risk-free rate of interest for the next year is r.

(i) Value a European Put on this asset with one year to maturity and a strike price of Rs 42, under the following scenarios:

• r = 5%, %

(b) r = 10%, p = 90%

Use a different approach for each answer.

(ii) In what direction is the value of the put likely to change under the following scenarios (justify your answers): (a) r remains constant, but p increases

(b) r increases and p increases (explain in context of a replicating portfolio)

(iii) Assume 4 scenarios where r = 5% and p is either 90%, 66%, 50% or 25% and another 4 scenarios where r = 10% and p is either 90%, 66%, 50% or 25%. Which of these 8 scenarios are plausible models of an investment universe populated by non-satiated risk-averse investors? Explain.

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