Financial Risk Management Formula.docx

Formula Sheet for Financial Risk Management Formulae Financial Basics Compounding Factor (future value of an interest factor r% for time t): Discount Factor (present value of an interest factor r% for time t): Future Annuity Factor (future value of an annuity factor for r% for n periods): Present Value Annuity Factor (present value of an annuity factor for r% for n periods): Covered Arbitrage Cost of Carry Model Simple Interest Compound Interest or Arbitrage Channel Implied Forward Rate Compound Interest Simple Interest Forward Rate Agreement Settlement Terms Synthetic Agreement for Forward Exchange Settlement Terms Exchange Rate Agreement Forward Exchange Agreement Hedge Sensitivity Ratio Fair Value of an At-market Swap Spot or Zero-Coupon Rate (Zi) derived from the par yield curve Option Pricing Option Delta Amount Borrowed Risk-Neutral Probability Value of Call with One Period to Expiry Value of Call with Two Periods to Expiry Binomial Model Pricing Inputs e = 2.71828 Black-Scholes Option Pricing Model Value of a Call and: Value for a Put Standard Deviation of Returns or equivalently: Approximation Formula for Implied Volatility ? = 3.14159 Polynomial Approximation to the Normal Distribution Option Sensitivities Adjustments to Delta European-style Call Option on a Stock Index with a Dividend Yield (d) European-style Put Option on a Stock Index with a Dividend Yield (d) European-style Call Option on a Futures Contract European-style Put Option on a Futures Contract European-style Call Option on a Currency European-style Put Option on a Currency Significance of N(d2) Lambda/Elasticity Gamma and Computational formula: Theta European-style calls: European-style puts: European-style call with a dividend yield: European-style put with a dividend yield: Rho Rho for calls: Rho for puts: Vega Underlier paying a continuous dividend: Adjustments to the Option Pricing Model Continuous Dividend Adjustment Model (Merton) Call option: Put option: and: Currency Options Call option on currency: Put option on currency: where: Currency Options on the Forward Price Call option: Put option: where: Options on Futures Futures call: Futures put: where: Commodity Options Call on a commodity: Put on a commodity: where: American-style Option Adjustment and: where: Hedging Minimum Variance Hedge Ratio Hedging Effectiveness Futures Spread Equity Hedging Constant Proportions Portfolio Insurance Hedge Ratio for Index Options Duration Measures Macaulay’s Duration Duration years: Computational Formula: Modified Duration Approximation Equation for Modified Duration Convexity Computational formula for deriving convexity: Approximation Equation for Convexity Portfolio Duration Price Value of a Basis Point M2