Derivatives Analysis & Valuation

Derivatives are contracts whose value is derived from an underlying — a

stock, index, interest rate, currency, or commodity. AFM tests four

instruments (forwards, futures, options, swaps) and three valuation lenses

(no-arbitrage forward pricing, put-call parity, binomial / Black-Scholes for

options).

1. The four basic instruments

2. Forward / futures pricing — the no-arbitrage rule

For a non-dividend-paying asset:

F = S × e^(r × T) (continuous compounding)

F = S × (1 + r × T) (simple)

If the actual forward deviates from this, an arbitrage opportunity exists —

borrow / lend the difference and lock in a riskless profit.

For an asset paying a known dividend yield q:

F = S × e^((r − q) × T)

For a currency (Interest Rate Parity, repeated from forex chapter):

F = S × (1 + r_dom × t) / (1 + r_for × t)

3. Options — payoff and pricing

3.1 Payoff at expiry

S = spot at expiry, K = strike.

3.2 Intrinsic value vs time value

Option premium = Intrinsic value + Time value

Intrinsic value:

• •Call: max(S − K, 0)
• •Put: max(K − S, 0)

Time value is the remaining premium — pure optionality. Decays to zero at

expiry (Theta).

3.3 Moneyness

3.4 Put-Call parity (European options, non-dividend)

C − P = S − K × e^(−r × T)

This relationship must hold at all times — any deviation creates an

arbitrage. ICAI loves to test this: give 3 of (C, P, S, K, r) and ask the 4th.

3.5 The two pricing models you must know

Binomial model:

1. Up factor u, down factor d, risk-free rate r per period.
2. Risk-neutral probability p = (e^(r×t) − d) / (u − d).
3. Option value at each node = expected payoff under p discounted by r.

Best for American options and path-dependent payoffs.

Black-Scholes (European, non-dividend, log-normal):

Call = S × N(d₁) − K × e^(−r×T) × N(d₂)

d₁ = [ln(S/K) + (r + σ²/2) × T] / (σ × √T)

d₂ = d₁ − σ × √T

N(·) is the standard normal CDF.

Inputs: S, K, T, r, σ. Five numbers. Get any one wrong and the answer flips.

4. The Greeks (sensitivities)

Delta:

• •Long call: 0 to +1
• •Long put: −1 to 0

5. Swaps — equivalent to a strip of forwards

Most common in AFM: plain vanilla interest rate swap.

• •Party A pays fixed, receives floating.
• •Party B pays floating, receives fixed.
• •Net cash settles each period based on notional × rate differential.

Use case: Indian firm with floating-rate ECB loan swaps to fixed via a CCBS

(cross-currency basis swap) to lock its INR cost.

Currency swap = swap of principal and interest in two different currencies.

Treat the principal exchange at start and end as two forward contracts.

6. ICAI exam patterns

Derivatives appears in almost every attempt. Total weight: 12–16 marks

across compulsory + optional questions.

7. The 60+ marks topper convention

• •Always state the convention — continuous vs simple compounding, days

in year (360 vs 365). Examiners dock for unstated assumptions.

• •Draw the option payoff diagram when asked about a strategy

(straddle, strangle, collar) — even when not strictly required. Visible

reasoning earns marks.

• •For binomial, draw the lattice — each node labelled with stock and

option value.

• •For put-call parity arbitrage, identify the action — "Buy the

underpriced call, sell the overpriced put, short the stock, invest PV of

K at r" — the four-step recipe.

• •Box the final option value / arbitrage profit.