Financial Derivatives December 2026
Q.1: You are asked to price a European call option on a stock with a two-step binomial model. The stock price is Rs.400; strike price is Rs.420; each period (of 2 months) the stock can go up by 12% (u = 1.12) or down by 7% (d = 0.93); the risk-free annual rate is 8% (assume discrete compounding per 2-month period). However, regulatory rules require option writers to set aside margin capital proportional to the worst-case payoff scenario at expiry, discounted at the risk-free rate. Construct the binomial tree with all possible payoffs, calculate risk-neutral probabilities, value the option, and also compute the amount of capital that must be set aside today according to the regulatory rule. Show all calculations for tree construction, discounting, probability, option price, and regulatory margin.
Answer:
Introduction:
The right but no obligation is given to the purchaser of the European call option to buy the underlying security at the agreed price at expiry date. In the given problem, the current stock price is Rs.400, and the strike price is Rs.420. The option has a two-step life, with each step representing 2 months. Further, during each 2-month period, the stock price can rise by 12% or fall by 7%. Therefore, it is possible to develop a two-step binomial tree for stock prices and option values.
Risk-Free Interest Rate = 8% per year using discrete compounding. First, we need to convert it into a 2-month rate and then use the up and down factors to determine the risk-neutral probabilities and the call option value. Further, Regulation requires that the writer of the option maintains a margin account with the value of the option at expiry time discounted at risk-free rate. Thus, the calculation of the required capital is separate from the calculation of the value of the option.
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Q.2 (A): An investor constructs a straddle by simultaneously buying a 1-month call option and a 1-month put option on Nifty, both with a strike price of Rs.17,000. The call option premium is Rs.325 and the put option premium is Rs.240. The lot size is 50 units. Determine (a) the exact profit or loss for the investor at expiry if Nifty closes at Rs.16,100, (b) the minimum Nifty closing price that would maximize the loss for this strategy, and (c) the total number of distinct Nifty closing prices (to the nearest integer) between 0 and 34,000 (inclusive) that would result in a net profit for the straddle strategy. Assume fractional prices are not possible and ignore transaction costs and taxes.
Answer:
Introduction:
Straddle strategy is made up of purchasing both call and put options at the same time using the same period of expiration and strike price. It is employed when the investor expects substantial movement in the underlying index but is unsure about the direction in which it will move. In this case, an investor has gone long on Nifty by purchasing a call and a put with a strike price of ₹17,000. The total premium paid by the investor is ₹565 per Nifty unit. Since the lot size is 50 units, the total cost to the investor is ₹28,250. The profit or loss will be determined by the distance between Nifty and the strike price at expiry.
Q.2 (B): Zenith Capital, a leading Indian investment firm, recently faced a major challenge when a key counterparty defaulted on its derivatives obligations amid market volatility. The incident exposed gaps in Zenith’s risk management systems, particularly regarding illiquid positions and operational controls. To respond, the firm strengthened liquidity buffers, improved controls, and implemented stricter margin requirements. As global regulators like SEBI, CFTC, and BIS increase their oversight and enforce new transparency standards, Zenith must evaluate which risk management practices are most effective and align with ethical and compliance expectations. Evaluate Zenith Capital’s revised risk management approach in mitigating credit, liquidity, and operational risks following the counterparty default. Considering global best practices and recent regulatory actions, how effective are their strategies in both meeting regulatory compliance and fostering market confidence? Justify any further improvements you would recommend.
Answer:
Introduction:
The default situation of Zenith Capital’s counterparty highlights the importance of risk management to an investment firm in the field of derivatives. A default event triggers risks of credit, liquidity and operations. Hence, the decision of Zenith to improve the liquidity cushions, enhance control activities and implement stricter margins is appropriate and will affect the risks from future defaults. Nevertheless, risk management needs to be done correctly to meet the requirements of regulators. Also, constant monitoring, reporting and ethical operations are needed to build and maintain the trust of stakeholders.