Description

Financial Derivatives

Dec 2026 Examination

 

Q1 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. (10 Marks)

Ans 1.

Introduction

This European call option needs to be priced using a two-step binomial model, where the underlying stock can move up or down by a fixed percentage in each of the two two-month periods that make up the option’s remaining life. Beyond finding the option’s fair value today, the regulator also requires option writers to set aside margin capital based on the worst possible payoff the option could produce at expiry, discounted back to the present. Building the binomial tree, calculating the risk-neutral probabilities, and valuing the option through backward induction

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Q2 (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. (5 Marks)

Ans 2(A).

Introduction

This investor has built a straddle on Nifty by buying both a call and a put at the same strike price, a strategy that profits from a large price movement in either direction but loses money if the index stays close to the strike at expiry. Working out the exact profit or loss at a given closing price, the point of maximum loss, and the count of profitable closing prices all depend on how the combined payoff behaves across the full range of outcomes.

Concept and Application

Combined Payoff of a Straddle

A straddle combines a long call and a long put at the same strike, so its payoff at expiry equals

 

 

Q2 (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. (5 Marks)

Ans 2(B).

Introduction

Zenith Capital’s exposure to a counterparty default revealed real weaknesses in how the firm managed illiquid positions and internal operational controls. In response, the firm strengthened its liquidity buffers, tightened controls and introduced stricter margin requirements, steps that directly target the credit, liquidity and operational risks exposed by the incident. Evaluating how effective these revised practices are, in meeting regulatory expectations and rebuilding market