Description Usage Arguments Details Value Note Author(s) References Examples

A collection and description of functions to valuate
basic American options. Approximative formulas for
American calls are given for the Roll, Geske and
Whaley Approximation, for the Barone-Adesi and Whaley
Approximation, and for the Bjerksund and Stensland
Approximation.

The functions are:

`RollGeskeWhaleyOption` | Roll, Geske and Whaley Approximation, |

`BAWAmericanApproxOption` | Barone-Adesi and Whaley Approximation, |

`BSAmericanApproxOption` | Bjerksund and Stensland Approximation. |

1 2 3 4 5 6 |

`b` |
the annualized cost-of-carry rate, a numeric value; e.g. 0.1 means 10% pa. |

`D` |
a single dividend with time to dividend payout |

`description` |
a character string which allows for a brief description. |

`r` |
the annualized rate of interest, a numeric value; e.g. 0.25 means 25% pa. |

`S` |
the asset price, a numeric value. |

`sigma` |
the annualized volatility of the underlying security, a numeric value; e.g. 0.3 means 30% volatility pa. |

`Time` |
the time to maturity measured in years, a numeric value. |

`time1, Time2` |
[RollGeskeWhaley*] - the first value measures time to dividend payout in years, e.g. 0.25 denotes a quarter, and the second value measures time to maturity measured in years, a numeric value; e.g. 0.5 means 6 months. |

`title` |
a character string which allows for a project title. |

`TypeFlag` |
a character string either "c" for a call option or a "p" for a put option. |

`X` |
the exercise price, a numeric value. |

**Roll-Geske-Whaley Option:**

The function `RollGeskeWhaleyOption`

valuates American calls
on a stock paying a single dividend with specified time to dividend
payout according to the pricing formula derived by Roll, Geske and
Whaley (1977).

`Approximations for American Options:`

The function `BSAmericanApproxOption`

valuates American calls
or puts on an underlying asset for a given cost-of-carry rate
according to the quadratic approximation method due to Barone-Adesi
and Whaley (1987). The function `BSAmericanApproxOption`

valuates
American calls or puts on stocks, futures, and currencies due to
the approximation method of Bjerksund and Stensland (1993).

`RollGeskeWhaleyOption`

`BAWAmericanApproxOption`

return the option price, a numeric value.

`BSAmericanApproxOption`

returns a list with the following two elements: `Premium`

the
option price, and `TriggerPrice`

the trigger price.

The functions implement the algorithms to valuate basic American options as described in Chapter 1.4 of Haug's Option Guide (1997).

Diethelm Wuertz for the Rmetrics **R**-port.

Barone-Adesi G., Whaley R.E. (1987);
*Efficient Analytic Approximation of American Option Values*,
Journal of Finance 42, 301–320.

Bjerksund P., Stensland G. (1993);
*Closed Form Approximation of American Options*,
Scandinavian Journal of Management 9, 87–99.

Geske R. (1979);
*A Note on an Analytical Formula for Unprotected
American Call Options on Stocks with known Dividends*,
Journal of Financial Economics 7, 63–81.

Haug E.G. (1997);
*The Complete Guide to Option Pricing Formulas*,
Chapter 1, McGraw-Hill, New York.

Roll R. (1977);
*An Analytic Valuation Formula for Unprotected
American Call Options on Stocks with known Dividends*,
Journal of Financial Economics 5, 251–258.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 | ```
## All the examples are from Haug's Option Guide (1997)
## CHAPTER 1.4: ANALYTICAL MODELS FOR AMERICAN OPTIONS
## Roll-Geske-Whaley American Calls on Dividend Paying
# Stocks [Haug 1.4.1]
RollGeskeWhaleyOption(S = 80, X = 82, time1 = 1/4,
Time2 = 1/3, r = 0.06, D = 4, sigma = 0.30)
## Barone-Adesi and Whaley Approximation for American
# Options [Haug 1.4.2] vs. Black76 Option on Futures:
BAWAmericanApproxOption(TypeFlag = "p", S = 100,
X = 100, Time = 0.5, r = 0.10, b = 0, sigma = 0.25)
Black76Option(TypeFlag = "c", FT = 100, X = 100,
Time = 0.5, r = 0.10, sigma = 0.25)
## Bjerksund and Stensland Approximation for American Options:
BSAmericanApproxOption(TypeFlag = "c", S = 42, X = 40,
Time = 0.75, r = 0.04, b = 0.04-0.08, sigma = 0.35)
``` |

```
Loading required package: timeDate
Loading required package: timeSeries
Loading required package: fBasics
Rmetrics Package fBasics
Analysing Markets and calculating Basic Statistics
Copyright (C) 2005-2014 Rmetrics Association Zurich
Educational Software for Financial Engineering and Computational Science
Rmetrics is free software and comes with ABSOLUTELY NO WARRANTY.
https://www.rmetrics.org --- Mail to: info@rmetrics.org
Rmetrics Package fOptions
Pricing and Evaluating Basic Options
Copyright (C) 2005-2014 Rmetrics Association Zurich
Educational Software for Financial Engineering and Computational Science
Rmetrics is free software and comes with ABSOLUTELY NO WARRANTY.
https://www.rmetrics.org --- Mail to: info@rmetrics.org
Title:
Roll Geske Whaley Option
Call:
RollGeskeWhaleyOption(S = 80, X = 82, time1 = 1/4, Time2 = 1/3,
r = 0.06, D = 4, sigma = 0.3)
Parameters:
Value:
S 80
X 82
time1 0.25
Time2 0.333333333333333
r 0.06
D 4
sigma 0.3
Option Price:
4.38603
Description:
Wed Aug 16 12:46:01 2017
Title:
BAW American Approximated Option
Call:
BAWAmericanApproxOption(TypeFlag = "p", S = 100, X = 100, Time = 0.5,
r = 0.1, b = 0, sigma = 0.25)
Parameters:
Value:
TypeFlag p
S 100
X 100
Time 0.5
r 0.1
b 0
sigma 0.25
Option Price:
6.801362
Description:
Wed Aug 16 12:46:01 2017
Title:
Black 76 Option Valuation
Call:
Black76Option(TypeFlag = "c", FT = 100, X = 100, Time = 0.5,
r = 0.1, sigma = 0.25)
Parameters:
Value:
TypeFlag c
FT 100
X 100
Time 0.5
r 0.1
sigma 0.25
Option Price:
6.699709
Description:
Wed Aug 16 12:46:01 2017
Title:
BS American Approximated Option
Call:
BSAmericanApproxOption(TypeFlag = "c", S = 42, X = 40, Time = 0.75,
r = 0.04, b = 0.04 - 0.08, sigma = 0.35)
Parameters:
Value:
TypeFlag c
S 42
X 40
Time 0.75
r 0.04
b -0.04
sigma 0.35
TrigerPrice 57.5994499306841
Option Price:
5.270405
Description:
Wed Aug 16 12:46:01 2017
```

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