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DerivativesModule 2 of 2

Derivative Pricing and Valuation

5

Concepts

5

Formulas

1

Decisions

3

Quiz Questions

Key Concepts

5 concepts covered in this module.

No-Arbitrage Pricing

Derivatives priced so no riskless profit is possible. If mispriced, arbitrageurs act to restore equilibrium.

Replication

A derivative can be replicated by a portfolio of the underlying and risk-free asset. Replication cost = derivative price.

Cost of Carry

Forward price = Spot × (1+r)T + Storage - Convenience yield. For financial assets: F = S(1+r)T.

Put-Call Parity

c + PV(X) = p + S. Links call, put, bond, and stock prices. Violation = arbitrage opportunity.

Binomial Option Pricing

Model stock as up/down moves. Calculate option values at nodes. Discount back using risk-neutral probabilities.

Formulas

5 essential formulas for this module.

Forward Price (no income)

F0 = S0 × (1 + r)T

Where: S = spot, r = risk-free rate, T = time

Forward with Continuous Dividends

F0 = S0 × e(r-q)T

Where: q = continuous dividend yield

Put-Call Parity

c + PV(X) = p + S

Where: c = call, p = put, X = strike, S = stock

Risk-Neutral Probability

πu = (1 + r - d) / (u - d)

Where: u = up factor, d = down factor

Binomial Option Value

C = [πuCu + (1-πu)Cd] / (1+r)

Where: Discount expected payoff at risk-free rate

Decision Frameworks

1 decision frameworks to guide your analysis.

When is put-call parity violated?

  • If c + PV(X) ≠ p + S, arbitrage exists
  • Buy the cheap side, sell the expensive side

Mind Map

Visual overview of how concepts connect in this module.

Derivative Pricing
Principles
No-arbitrage
Replication
Risk-neutral pricing
Law of one price
Forward Pricing
F = S(1+r)^T
Cost of carry
Convenience yield
Storage costs
Put-Call Parity
c + PV(X) = p + S
European only
Arbitrage if violated
Binomial Model
Up/down factors
Risk-neutral prob
Backward induction
Option value at nodes
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No-Arbitrage Pricing

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Answer
Derivatives priced so no riskless profit is possible. If mispriced, arbitrageurs act to restore equilibrium.
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