Finance - Maple Programming Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Mathematics : Finance : Financial Instruments : Finance/ImpliedVolatility

Finance

  

ImpliedVolatility

  

compute the implied volatility for a European-style option

 

Calling Sequence

Parameters

Description

Examples

References

Compatibility

Calling Sequence

ImpliedVolatility(price, spot, strike, timetomaturity, riskfreerate, dividendyield, optiontype)

ImpliedVolatility(price, spot, payoff, timetomaturity, riskfreerate, dividendyield)

Parameters

price

-

algebraic expression; option price

spot

-

algebraic expression; spot price of the underlying asset

strike

-

algebraic expression; strike price

timetomaturity

-

algebraic expression; time to maturity (in years)

riskfreerate

-

algebraic expression; continuously compounded risk-free rate

dividendyield

-

algebraic expression; continuously compounded dividend yield

optiontype

-

call or put; option type

payoff

-

operator or procedure; payoff function

Description

• 

The ImpliedVolatility command computes the implied Black-Scholes volatility for a European-style option given its price.

• 

The parameter price is the option price.

• 

The parameter spot is the initial (current) value of the underlying asset.

• 

The parameter strike specifies the strike price of the option (if this is a call option or a put option). More general payoff can be specified using the payoff parameter. It must be specified in the form of an operator, which accepts one parameter (spot price at maturity) and returns the corresponding payoff.

• 

The riskfreerate and dividendyield parameters are the risk-free rate and the dividend yield. These parameters can be given in either the algebraic form or the operator form.

Examples

withFinance:

Compute implied volatilities for an asset with spot price S0=100. Assume that the risk-free rate is 5% and the dividend yield is 3%.

S100

S:=100

(1)

r0.05

r:=0.05

(2)

d0.03

d:=0.03

(3)

First you consider European call and put options with strike price K=100.

K100

K:=100

(4)

ImpliedVolatility15.0,S,100,1,r,d,'call'

0.3677816494

(5)

ImpliedVolatility15.0,S,t→maxt100,0,1,r,d

0.3677816498

(6)

ImpliedVolatility15.0,S,100,1,r,d,'put'

0.4189619392

(7)

ImpliedVolatility15.0,S,t→max100t,0,1,r,d

0.4189619390

(8)

In this example you consider a strangle.

&sigma;ImpliedVolatility15.0&comma;S&comma;t&rarr;piecewiset<90&comma;90t&comma;t<110&comma;0&comma;t110&comma;1&comma;r&comma;d

&sigma;:=0.3041486797

(9)

BlackScholesPriceS&comma;t&rarr;piecewiset<90&comma;90t&comma;t<110&comma;0&comma;t110&comma;1&comma;&sigma;&comma;r&comma;d

14.99999999

(10)

References

  

Hull, J., Options, Futures, and Other Derivatives, 5th. edition. Upper Saddle River, New Jersey: Prentice Hall, 2003.

Compatibility

• 

The Finance[ImpliedVolatility] command was introduced in Maple 15.

• 

For more information on Maple 15 changes, see Updates in Maple 15.

See Also

Finance[AmericanOption]

Finance[BlackScholesDelta]

Finance[BlackScholesGamma]

Finance[BlackScholesPrice]

Finance[BlackScholesRho]

Finance[BlackScholesTheta]

Finance[BlackScholesVega]

Finance[EuropeanOption]

Finance[LatticePrice]

Finance[LocalVolatility]

 


Download Help Document

Was this information helpful?



Please add your Comment (Optional)
E-mail Address (Optional)
What is ? This question helps us to combat spam