Financial library functions

Analytica User GuideText, Date, Math, and Financial FunctionsFinancial library functions

These financial functions are not built-in to Analytica, but are located in the Financial library installed with Analytica.

Calloption(S, X, T, r, theta)

Calculates the value of a call option using the Black-Scholes formula. For further information on the Black-Scholes model for option pricing see Basic Black-Scholes: Option Pricing and Trading by Timothy Falcon Crack.

Parameters:

S = price of security now

X = exercise price

T = time in years to exercise

r = risk-free interest rate

theta = volatility of security

Library: Financial (add-in library)

Syntax: Calloption(S, X, T, r, theta: Numeric)

Example:

Calloption(50, 50, 0.25, 0.05, 0.3) → 3.292

See also Calloption().

Putoption(S, X, T, r, theta)

Calculates the value of a put option using the Black-Scholes formula. For further information on the Black-Scholes model for option pricing see Basic Black-Scholes: Option Pricing and Trading by Timothy Falcon Crack.

Parameters:

S = price of security now

X = exercise price

T = time in years to exercise

r = risk-free interest rate

theta = volatility of security

Library: Financial (add-in library)

Syntax: Putoption(S, X, T, r, theta: Numeric)

Example:

Putoption(50, 50, 0.25, 0.05, 0.3) → 2.67

See also Putoption().

Capm(Rf, Rm, Beta)

Calculates the expected stock return under the Capital Asset Pricing Model (CAPM). For more, see Black, F., Jensen, M., and Scholes, M. "The Capital Asset Pricing Model: Some Empirical Tests,” in M. Jensen ed., Studies in the Theory of Capital Markets. (1972).

Parameters:

Rf = risk free rate

Rm = market return

Beta = beta of individual stock. Beta is the relative marginal contribution of the stock to the market return, defined as the ratio of the covariance between the stock return and market return, to the variance in the market return.

Library: Financial (add-in library)

Syntax: Capm(Rf, Rm, Beta: Numeric)

Example:

Capm(8%, 12%, 1.5) → 0.14

See also Capm().

CostCapme(rOpp, rD, Tc, L)

This function calculates Miles and Ezzell’s (M/E) formula for adjusting the weighted average cost of capital for financial leverage. The M/E formula works when the firm adjusts its future borrowing to keep debt proportions constant.

Parameters:

rOpp = opportunity cost of capital

rD = expected return on debt

Tc = net tax saving per dollar of interest paid. This is difficult to pin down in practice and is usually taken as the corporate tax rate.

L = debt-to-value ratio

Library: Financial (add-in library)

Syntax: CostCapme(rOpp, rD, Tc, L: Numeric)

Example:

CostCapme(14%, 8%, 35%, 0.5) → 0.1252

See also CostCapme().

CostCapmm(rAllEq, Tc, L)

This function calculates Modigliani and Miller’s (M/M) formula for adjusting the weighted average cost of capital for financial leverage. The M/M formula works for any project that is expected to:

1. Generate a level, perpetual cash flow.
2. Support fixed permanent debt.

Parameters:

rAllEq = cost of capital under all-equity financing

Tc = net tax saving per dollar of interest paid. This is difficult to pin down in practice and is usually taken as the corporate tax rate.

L = debt-to-value ratio

Library: Financial (add-in library)

Syntax: CostCapmm(rAllEq, Tc, L: Numeric)

Example:

CostCapmm(20%, 35%, 0.4) → 0.172

See also CostCapmm().

Implied_volatility_c(S, X, T, r, p)

This function calculates the implied volatility of a call option, based on using the Black-Scholes formula for options.

Parameters:

S = price of security now

X = exercise price

T = time in years to exercise

r = risk-free interest rate

p = option price

Library: Financial (add-in library)

Syntax: Implied_volatility_c(S, X, T, r, p: atomic numeric)

Example:

Implied_volatility_c(50, 35, 4, 6%, 15) &rarr 3.052e-005

See also Implied_volatility_c().

Implied_volatility_p(S, X, T, r, p)

This function calculates the implied volatility of a put option, based on using the Black-Scholes formula for options.

Parameters:

S = price of security now

X» = exercise price

T = time in years to exercise

r = risk-free interest rate

p = option price

Library: Financial (add-in library)

Syntax: Implied_volatility_p(S, X, T, r, p: atomic numeric)

Example:

Implied_volatility_p(50, 35, 4, 6%, 15) → 9.416e-001

See also Implied_volatility_p().

Pvperp(C, rate)

Pvperp() calculates the present value of a perpetuity (a bond that pays a constant amount in perpetuity).

Parameters:

C = constant payment amount

rate = interest rate per period

Library: Financial (add-in library)

Syntax: Pvperp(C, rate: Numeric)

Example:

Pvperp(200, 8%) → 2500

Pvgperp(C1, rate, growth)

Pvgperp() calculates the present value of a growing perpetuity (a bond that pays an amount growing at a constant rate in perpetuity).

Parameters:

C1 = payment amount in year 1

rate = interest rate per period

growth = growth rate per period

Library: Financial (add-in library)

Syntax: Pvgperp(C1, rate, growth: Numeric)

Example:

Pvgperp(200, 8%, 6%) → 10K

Wacc(Debt, Equity, rD, rE, Tc)

Wacc() calculates the after-tax weighted average cost of capital, based on the expected return on a portfolio of all the firm’s securities. Used as a hurdle rate for capital investment.

Parameters:

Debt = market value of debt

Equity = market value of equity

rD = expected return on debt

rE = expected return on equity

Tc = corporate tax rate

Library: Financial (add-in library)

Syntax: Wacc(Debt, Equity, rD, rE, Tc: Numeric)

Example:

Wacc(1M, 3M, 8%, 16%, 35%) → 0.133

See Also

• Financial Library.ana
• Calloption]()
• Putoption()
• Capm()
• CostCapme()
• CostCapmm()
• Implied_volatility_c()
• Implied_volatility_p()
• Pvperp()
• Pvgperp()
• Wacc()
• Analytica Libraries and Templates

Financial functionsFinancial library functionsUser Interfaces for End Users