Question

The current price of the underlying is 100 pesos and the volatility is 30 percent per year. The risk-free interest rate is 6 percent per year. Consider a one-year European call option on this underlying priced at 100 weight exercise.

i. Divide the period of 1 year into 2 intervals of 6 months each and use the tree. multiplicative with u and d as in the previous question. Calculate the risk-
neutral probabilities. Shows that the option value is 13.718486. Assume that the option has a market value of 14. Considering that the market
ii. is described by the tree in part (1), there must be an arbitration opportunity. Explain in detail (specifying all movements cough) how you could take advantage of the wrong market price to get a benefit without risk.

Answer 1

The question involves calculating the value of a call option using a binomial tree, exploring risk-neutral probabilities, and identifying an arbitrage opportunity based on market prices. It also touches on the concepts of interest rate risk, opportunity cost, and present discounted value in bond pricing.

Step-by-step explanation:

The student's question concerns calculating the value of a European call option using a binomial tree and identifying an arbitrage opportunity given the market price of the option. When assessing options or bonds, it's important to consider risk-free interest rate, market interest rate, and volatility. The question also involves determining risk-neutral probabilities and identifying discrepancies between theoretical and market prices to exploit for arbitrage. For example, if the bond's market interest rate rises above the bond's coupon rate, the bond price will fall to offer investors a comparable yield to that of newer issues with higher coupon rates. This exemplifies interest rate risk and its impact on bond pricing. The question also illustrates the concept of opportunity cost in scenarios where current holdings become less attractive compared to new offerings. In the scenario provided, an investor should not pay more than the present discounted value for future payments when the market interest rate exceeds the interest rate of the bond held. This calculation allows one to determine what amount in the present equals a certain future payment, inclusive of the prevailing interest rate.