BCC {BCC1997} | R Documentation |

## Calculation of Option Prices Based on a Universal Solution

### Description

This is a function to calculate the prices of European options based on the universal solution provided by Bakshi, Cao and Chen (1997) <doi:10.1111/j.1540-6261.1997.tb02749.x>. This solution takes stochastic volatility, stochastic interest and random jumps into consideration. Please cite their work if this package is used.

### Usage

```
BCC(kappav, kappar, thetav, thetar, sigmav, sigmar, muj, sigmaj, rho, lambda,
S0, K, V0, R0, t)
```

### Arguments

`kappav` |
Speed of convergence on variance |

`kappar` |
Speed of convergence on risk free rate |

`thetav` |
Long-term variance |

`thetar` |
Long-term risk free rate |

`sigmav` |
Volatility of variance |

`sigmar` |
Volatility of risk free rate |

`muj` |
Jump size |

`sigmaj` |
Volatility of jumps |

`rho` |
Correlation between underlying price and variance |

`lambda` |
Jump intensity |

`S0` |
Initial/Current underlying price |

`K` |
Strike price |

`V0` |
Initial/Current variance |

`R0` |
Initial/Current risk free rate |

`t` |
Time to maturity |

### Value

Call: return the price of the European call oprion

Put: return the price of the European put oprion

### Note

Please notice each parameter has its "reasonable range". e.g. volatilities cannot be zero or smaller than zero, please input 0.0000001 when they are zero.

### Examples

```
BCC(kappav=0,kappar=0,thetav=0,thetar=0,sigmav=0.0000001,sigmar=0.0000001,muj=0,
sigmaj=0.0000001,rho=0,lambda=0,S0=100,K=100,V0=0.04,R0=0.01,t=1)
BCC(kappav=0.5,kappar=0,thetav=0.025,thetar=0,sigmav=0.09,sigmar=0.0000001,muj=0,
sigmaj=0.0000001,rho=0.1,lambda=0,S0=100,K=100,V0=0.04,R0=0.01,t=1)
```

*BCC1997*version 0.1.1 Index]