Corporate Financial Policy

CFP Cheatsheet — Jens-Fabian Goetzmann

Pg. 1

P2 Mar/Apr 2012 Singapore — Prof. Pierre Hillion / Theo Vermaelen

Derivatives

Definitions Derivative: An instrument whose value depends on the value of another instrument Type 1 Type 2 • Forwards (OTC) • Options (ET, OTC (more important)) • Futures (ET) • Swaps (OTC, most important derivative) Commitments between two parties involved • Long forward—commitment to buy • Short forward—commitment to sell → symmetric contract Categories: • OTC (over the counter) – private contract • ET (exchange traded) Significant differences: • Counter-party risk: much more for OTC as opposed to ET • Liquidity: closing OTC contract is difficult Notation Time: today=0, maturity=������ Exercise price: ������ Spot price: ������ (������! , ������! ) Call premium: ������ (������! , ������! ) Forward price: ������ Put premium: ������ (������! , ������! ) One party has a right (long option), other party has a commitment (short option, contingent liability) → asymmetric contract

Put-Call Parity At maturity: ������! + ������! = ������! + ������ At time 0: ������! + ������! = ������! + ������������[������] Asset + Put = Call + Risk-free bond Special cases: • ������ = ������! (ATM-S = at-the-money spot) • ������! = ������������ ������ , then ������! = ������! (ATM-F = at-the-money forward) Option Valuation—By Arbitrage Construct portfolio so that it is riskless at maturity (given range for ������! ): Long 1 asset, Short ������ calls Calculate payoffs at maturity and choose ������ so that portfolio is riskless Portfolio value today: ������! − ������������! = ������������[������������������������������������������������������  ������������������������������  ������������  ������������������������������������������������] (use risk-free rate) Option Valuation using RNV (Risk Neutral Valuation) Inputs required: Spot price ������! Strike price ������ Maturity ������ Risk-free rate ������! Range (volatility) Step 1: construct binomial tree...