Calculate Bachelier model implied volatility

Description

Calculate Bachelier model implied volatility

Usage

BachelierImpvol(
  price,
  strike = forward,
  spot,
  texp = 1,
  intr = 0,
  divr = 0,
  cp = 1L,
  forward = spot * exp(-divr * texp)/df,
  df = exp(-intr * texp)
)

Arguments

Value

Bachelier implied volatility

References

Choi, J., Kim, K., & Kwak, M. (2009). Numerical Approximation of the Implied Volatility Under Arithmetic Brownian Motion. Applied Mathematical Finance, 16(3), 261-268. doi: 10.1080/13504860802583436

See Also

BachelierPrice

Examples

spot <- 100
strike <- 100
texp <- 1.2
sigma <- 20
intr <- 0.05
price <- 20
FER::BachelierImpvol(price, strike, spot, texp, intr=intr)

Calculate Bachelier model option price

Description

Calculate Bachelier model option price

Usage

BachelierPrice(
  strike = forward,
  spot,
  texp = 1,
  sigma,
  intr = 0,
  divr = 0,
  cp = 1L,
  forward = spot * exp(-divr * texp)/df,
  df = exp(-intr * texp)
)

Arguments

Value

option price

References

Choi, J., Kim, K., & Kwak, M. (2009). Numerical Approximation of the Implied Volatility Under Arithmetic Brownian Motion. Applied Mathematical Finance, 16(3), 261-268. doi: 10.1080/13504860802583436

See Also

BachelierImpvol

Examples

spot <- 100
strike <- seq(80,125,5)
texp <- 1.2
sigma <- 20
intr <- 0.05
FER::BachelierPrice(strike, spot, texp, sigma, intr=intr)

Calculate Black-Scholes implied volatility

Description

Calculate Black-Scholes implied volatility

Usage

BlackScholesImpvol(
  price,
  strike = forward,
  spot,
  texp = 1,
  intr = 0,
  divr = 0,
  cp = 1L,
  forward = spot * exp(-divr * texp)/df,
  df = exp(-intr * texp)
)

Arguments

Value

Black-Scholes implied volatility

References

Giner, G., & Smyth, G. K. (2016). statmod: Probability Calculations for the Inverse Gaussian Distribution. The R Journal, 8(1), 339-351. doi: 10.32614/RJ-2016-024

See Also

BlackScholesPrice

Examples

spot <- 100
strike <- 100
texp <- 1.2
sigma <- 0.2
intr <- 0.05
price <- 20
FER::BlackScholesImpvol(price, strike, spot, texp, intr=intr)

Calculate Black-Scholes option price

Description

Calculate Black-Scholes option price

Usage

BlackScholesPrice(
  strike = forward,
  spot,
  texp = 1,
  sigma,
  intr = 0,
  divr = 0,
  cp = 1L,
  forward = spot * exp(-divr * texp)/df,
  df = exp(-intr * texp)
)

Arguments

Value

option price

References

Black, F., & Scholes, M. (1973). The Pricing of Options and Corporate Liabilities. Journal of Political Economy, 81(3), 637-654. doi: 10.1086/260062

Black, F. (1976). The pricing of commodity contracts. Journal of Financial Economics, 3(1), 167-179. doi: 10.1016/0304-405X(76)90024-6

https://en.wikipedia.org/wiki/Black-Scholes_model

See Also

BlackScholesImpvol

Examples

spot <- 100
strike <- seq(80,125,5)
texp <- 1.2
sigma <- 0.2
intr <- 0.05
FER::BlackScholesPrice(strike, spot, texp, sigma, intr=intr)

Calculate the mass at zero under the CEV model

Description

Calculate the mass at zero under the CEV model

Usage

CevMassZero(
  spot,
  texp = 1,
  sigma,
  beta = 0.5,
  intr = 0,
  divr = 0,
  forward = spot * exp(-divr * texp)/df,
  df = exp(-intr * texp)
)

Arguments

Value

mass at zero

Examples

spot <- 100
texp <- 1.2
beta <- 0.5
sigma <- 2
FER::CevMassZero(spot, texp, sigma, beta)

Calculate the constant elasticity of variance (CEV) model option price

Description

Calculate the constant elasticity of variance (CEV) model option price

Usage

CevPrice(
  strike = forward,
  spot,
  texp = 1,
  sigma,
  beta = 0.5,
  intr = 0,
  divr = 0,
  cp = 1L,
  forward = spot * exp(-divr * texp)/df,
  df = exp(-intr * texp)
)

Arguments

Value

option price

References

Schroder, M. (1989). Computing the constant elasticity of variance option pricing formula. Journal of Finance, 44(1), 211-219. doi: 10.1111/j.1540-6261.1989.tb02414.x

Examples

spot <- 100
strike <- seq(80,125,5)
texp <- 1.2
beta <- 0.5
sigma <- 2
FER::CevPrice(strike, spot, texp, sigma, beta)

Calculate the option price under the NSVh model with lambda=1 (Choi et al. 2019)

Description

Calculate the option price under the NSVh model with lambda=1 (Choi et al. 2019)

Usage

Nsvh1Choi2019(
  strike = forward,
  spot,
  texp = 1,
  sigma,
  vov = 0,
  rho = 0,
  intr = 0,
  divr = 0,
  cp = 1L,
  forward = spot * exp(-divr * texp)/df,
  df = exp(-intr * texp)
)

Arguments

Value

BS volatility or option price based on cp

References

Choi, J., Liu, C., & Seo, B. K. (2019). Hyperbolic normal stochastic volatility model. Journal of Futures Markets, 39(2), 186–204. doi: 10.1002/fut.21967

Examples

spot <- 100
strike <- seq(80,125,5)
texp <- 1.2
sigma <- 20
vov <- 0.2
rho <- -0.5
strike <- seq(0.1, 2, 0.1)

FER::Nsvh1Choi2019(strike, spot, texp, sigma, vov, rho)

Calculate the equivalent BS volatility (Hagan et al. 2002) for the Stochatic-Alpha-Beta-Rho (SABR) model

Description

Calculate the equivalent BS volatility (Hagan et al. 2002) for the Stochatic-Alpha-Beta-Rho (SABR) model

Usage

SabrHagan2002(
  strike = forward,
  spot,
  texp = 1,
  sigma,
  vov = 0,
  rho = 0,
  beta = 1,
  intr = 0,
  divr = 0,
  cp = NULL,
  forward = spot * exp(-divr * texp)/df,
  df = exp(-intr * texp)
)

Arguments

Value

BS volatility or option price based on cp

References

Hagan, P. S., Kumar, D., Lesniewski, A. S., & Woodward, D. E. (2002). Managing Smile Risk. Wilmott, September, 84-108.

Examples

sigma <- 0.25
vov <- 0.3
rho <- -0.8
beta <- 0.3
texp <- 10
strike <- seq(0.1, 2, 0.1)
FER::SabrHagan2002(strike, 1, texp, sigma, vov, rho, beta)
FER::SabrHagan2002(strike, 1, texp, sigma, vov, rho, beta, cp=1)

Spread option under the Bachelier model

Description

The payout of the spread option is max(S1_T - S2_T - K, 0) where S1_T and S2_T are the prices at expiry T of assets 1 and 2 respectively and K is the strike price.

Usage

SpreadBachelier(
  strike = 0,
  spot1,
  spot2,
  texp = 1,
  sigma1,
  sigma2,
  corr,
  intr = 0,
  divr1 = 0,
  divr2 = 0,
  cp = 1L,
  forward1 = spot1 * exp(-divr1 * texp)/df,
  forward2 = spot2 * exp(-divr2 * texp)/df,
  df = exp(-intr * texp)
)

Arguments

Value

option price

Examples

FER::SpreadBachelier((-2:2)*10, 100, 120, 1.3, 20, 36, -0.5)

Spread option pricing method by Bjerksund & Stensland (2014)

Description

The payout of the spread option is max(S1_T - S2_T - K, 0) where S1_T and S2_T are the prices at expiry T of assets 1 and 2 respectively and K is the strike price.

Usage

SpreadBjerksund2014(
  strike = 0,
  spot1,
  spot2,
  texp = 1,
  sigma1,
  sigma2,
  corr,
  intr = 0,
  divr1 = 0,
  divr2 = 0,
  cp = 1L,
  forward1 = spot1 * exp(-divr1 * texp)/df,
  forward2 = spot2 * exp(-divr2 * texp)/df,
  df = exp(-intr * texp)
)

Arguments

Value

option price

References

Bjerksund, P., & Stensland, G. (2014). Closed form spread option valuation. Quantitative Finance, 14(10), 1785–1794. doi: 10.1080/14697688.2011.617775

Examples

FER::SpreadBjerksund2014((-2:2)*10, 100, 120, 1.3, 0.2, 0.3, -0.5)

Kirk's approximation for spread option

Description

The payout of the spread option is max(S1_T - S2_T - K, 0) where S1_T and S2_T are the prices at expiry T of assets 1 and 2 respectively and K is the strike price.

Usage

SpreadKirk(
  strike = 0,
  spot1,
  spot2,
  texp = 1,
  sigma1,
  sigma2,
  corr,
  intr = 0,
  divr1 = 0,
  divr2 = 0,
  cp = 1L,
  forward1 = spot1 * exp(-divr1 * texp)/df,
  forward2 = spot2 * exp(-divr2 * texp)/df,
  df = exp(-intr * texp)
)

Arguments

Value

option price

References

Kirk, E. (1995). Correlation in the energy markets. In Managing Energy Price Risk (First, pp. 71–78). Risk Publications.

See Also

SwitchMargrabe

Examples

FER::SpreadKirk((-2:2)*10, 100, 120, 1.3, 0.2, 0.3, -0.5)

Margrabe's formula for exhange option price

Description

The payout of the exchange option is max(S1_T - S2_T, 0) where S1_T and S2_T are the prices at expiry T of assets 1 and 2 respectively.

Usage

SwitchMargrabe(
  spot1,
  spot2,
  texp = 1,
  sigma1,
  sigma2,
  corr,
  intr = 0,
  divr1 = 0,
  divr2 = 0,
  cp = 1L,
  forward1 = spot1 * exp(-divr1 * texp)/df,
  forward2 = spot2 * exp(-divr2 * texp)/df,
  df = exp(-intr * texp)
)

Arguments

Value

option price

References

Margrabe, W. (1978). The value of an option to exchange one asset for another. The Journal of Finance, 33(1), 177–186.

See Also

SpreadKirk

Examples

FER::SwitchMargrabe(100, 120, 1.3, 0.2, 0.3, -0.5)