Description Usage Arguments Details Value Note Author(s) References Examples
A collection and description of functions to valuate
lookback options. The payoff from a pathdependent
lookback call (put) depends on the exercise price
being set to the minimum (maximum) asset price achieved
during the life of the option. Thus, a lookback call
(put) allows the purchaser to buy (sell) the asset at
its minimum (maximum) price.
The functions are:
FloatingStrikeLookbackOption | Floating Strike Lookback Option, |
FixedStrikeLookbackOption | Fixed Strike Lookback Option, |
PTFloatingStrikeLookbackOption | PT Floating Strike Lookback Option, |
PTFixedStrikeLookbackOption | PT Fixed Strike Lookback Option, |
ExtremeSpreadOption | Extreme Spread Options. |
1 2 3 4 5 6 7 8 9 10 | FloatingStrikeLookbackOption(TypeFlag, S, SMinOrMax, Time, r,
b, sigma, title = NULL, description = NULL)
FixedStrikeLookbackOption(TypeFlag, S, SMinOrMax, X, Time, r,
b, sigma, title = NULL, description = NULL)
PTFloatingStrikeLookbackOption(TypeFlag, S, SMinOrMax, time1,
Time2, r, b, sigma, lambda, title = NULL, description = NULL)
PTFixedStrikeLookbackOption(TypeFlag, S, X, time1, Time2, r, b,
sigma, title = NULL, description = NULL)
ExtremeSpreadOption(TypeFlag, S, SMin, SMax, time1, Time2, r, b,
sigma, title = NULL, description = NULL)
|
b |
the annualized cost-of-carry rate, a numeric value; e.g. 0.1 means 10% pa. |
description |
a character string which allows for a brief description. |
lambda |
The |
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. |
SMax, SMin |
[ExtremeSpread*] - |
SMinOrMax |
the lowest price observed of the underlying in the case of the coll, or the highest price in the case of the put. A numeric value. |
Time |
the time to maturity measured in years, a numeric value; e.g. 0.5 means 6 months. |
time1, Time2 |
[PTFloatingStrikeLookback*] - |
title |
a character string which allows for a project title. |
TypeFlag |
usually a character string either |
X |
the exercise price, a numeric value. |
Floating Strike Lookback Options:
The lookback call (put) option gives the holder the right to buy (sell)
an asset at its lowest (highest) price observed during the life of the
option. This observed price is applied as the strike price. The payout
for a call option is essentially the asset price minus the minimum spot
price observed during the life of the option. The payout for a put option
is essentially the maximum spot price observed during the life of the
option minus the asset price. Therefore, a floating strike lookback
option is always in the money and should always be exercised. Floating
strike options can be priced analytically using a model introduced by
Goldman, Sosin, and Gatto (1979). Monte Carlo simulation is used for
the numerical calculation of a European style floating strike options.
[Haug's Book, Chapter 2.9.1]
Fixed Strike Lookback Options:
For a fixed strike lookback option, the strike price is known in advance.
The call option payoff is given by the difference between the maximum
observed price of the underlying asset during the life of the option and
the fixed strike price. The put option payoff is given by the difference
between the fixed strike price and the minimum observed price of the
underlying asset during the life of the option. A fixed strike lookback
call (put) option payoff is equal to that of a standard plain call (put)
option when the final asset price is the maximum (minimum) observed value
during the options life. Fixed strike lookback options can be priced
analytically using a model introduced by Conze and Viswanathan (1991).
[Haug's Book, Chapter 2.9.2]
Partial-Time Floating Strike Options:
For a partial-time floating strike lookback option, the lookback period
starts at time zero and ends at an arbitrary date before expiration.
Except for the partial lookback period, the option is similar to a
floating strike lookback option. The partial-time floating strike
lookback option is cheaper than a similar standard floating strike
lookback option. Partial-time floating strike lookback options can be
priced analytically using a model introduced by Heynen and Kat (1994).
[Haug's Book, Chapter 2.9.3]
Partial-Time Fixed Strike Options:
For a partial-time fixed strike lookback option, the lookback period
starts at a predetermined date after the initialization date of the
option. The partial-time fixed strike lookback call option payoff is
given by the difference between the maximum observed price of the
underlying asset during the lookback period and the fixed strike
price. The partial-time fixed strike lookback put option payoff is
given by the difference between the fixed strike price and the
minimum observed price of the underlying asset during the lookback
period. The partial-time fixed strike lookback option is cheaper than
a similar standard fixed strike lookback option. Partial-time fixed
strike lookback options can be priced analytically using a model
introduced by Heynen and Kat (1994).
[Haug's Book, Chapter 2.9.4]
Extreme Spread Options:
The time to maturity of an extreme spread option is divided into two
periods: one period starting at time zero and ending at some arbitrary
date, and another starting at that arbitrary date and ending at the
expiration date. A payoff at maturity of an extreme spread call (put)
option equals the positive part of the difference between the maximum
(minimum) value of the underlying asset of the second (first) period
and the maximum (minimum) value of the underlying asset of the first
(second) period.[1] The payoff at expiration of a reverse extreme
spread call (put) option equals the positive part of the difference
between the minimum (maximum) of the underlying asset of the second
(first) period and the minimum (maximum) value of the underlying asset
of the first (second) period. Extreme spread options can be priced
analytically using a model introduced by Bermin (1996).
[Haug's Book, Chapter 2.9.5]
The option price, a numeric value.
The functions implement the algorithms to valuate plain vanilla options as described in Chapter 2.9 of Haug's Book (1997).
Diethelm Wuertz for the Rmetrics R-port.
Bermin H.P. (1996b); Exotic Lookback Options: The case of Extreme Spread Options, Department of Economics, Lund University, Sweden.
Conze A., Viswanathan R. (1991); Path Dependent Options: The Case of Lookback Options, Journal of Finance 46, 1893–1907.
Goldmann B.M., Sosin H.B., Gatto M.A. (1993); Path Dependent Options: Buy at the Low, Sell at the High, Journal of Finance 34, 1111.
Haug E.G. (1997); The Complete Guide to Option Pricing Formulas, McGraw-Hill, New York.
Heynen R.C., Kat H.M. (1994); Selective Memory, Risk Magazine 7, 1994.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 | ## Examples from Chapter 2.9 in E.G. Haug's Option Guide (1997)
## Floating Strike Lookback Option [2.9.1]:
FloatingStrikeLookbackOption(TypeFlag = "c", S = 120,
SMinOrMax = 100, Time = 0.5, r = 0.10, b = 0.10-0.06,
sigma = 0.30)
## Fixed Strike Lookback Option [2.9.2]:
FixedStrikeLookbackOption(TypeFlag = "c", S = 100,
SMinOrMax = 100, X = 105, Time = 0.5, r = 0.10, b = 0.10,
sigma = 0.30)
## Partial Time Floating Strike Lookback Option [2.9.3]:
PTFloatingStrikeLookbackOption(TypeFlag = "p", S = 90,
SMinOrMax = 90, time1 = 0.5, Time2 = 1, r = 0.06, b = 0.06,
sigma = 0.20, lambda = 1)
## Partial Time Fixed Strike Lookback Option [2.9.4]:
PTFixedStrikeLookbackOption(TypeFlag = "c", S = 100, X = 90,
time1 = 0.5, Time2 = 1, r = 0.06, b = 0.06, sigma = 0.20)
## Extreme Spread Option [2.9.5]:
ExtremeSpreadOption(TypeFlag = "c", S = 100, SMin = NA,
SMax = 110, time1 = 0.5, Time2 = 1, r = 0.1, b = 0.1,
sigma = 0.30)
ExtremeSpreadOption(TypeFlag = "cr", S = 100, SMin = 90,
SMax = NA, time1 = 0.5, Time2 = 1, r = 0.1, b = 0.1,
sigma = 0.30)
|
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Loading required package: fOptions
Rmetrics Package fOptions
Pricing and Evaluating Basic Options
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Title:
Floating Strike Lookback Option
Call:
FloatingStrikeLookbackOption(TypeFlag = "c", S = 120, SMinOrMax = 100,
Time = 0.5, r = 0.1, b = 0.1 - 0.06, sigma = 0.3)
Parameters:
Value:
TypeFlag c
S 120
SMinOrMax 100
Time 0.5
r 0.1
b 0.04
sigma 0.3
Option Price:
25.35334
Description:
Tue Nov 13 20:02:02 2018
Title:
Fixed Strike Lookback Option
Call:
FixedStrikeLookbackOption(TypeFlag = "c", S = 100, SMinOrMax = 100,
X = 105, Time = 0.5, r = 0.1, b = 0.1, sigma = 0.3)
Parameters:
Value:
TypeFlag c
S 100
SMinOrMax 100
X 105
Time 0.5
r 0.1
b 0.1
sigma 0.3
Option Price:
15.85121
Description:
Tue Nov 13 20:02:02 2018
Title:
Partial Time Floating Strike Lookback Option
Call:
PTFloatingStrikeLookbackOption(TypeFlag = "p", S = 90, SMinOrMax = 90,
time1 = 0.5, Time2 = 1, r = 0.06, b = 0.06, sigma = 0.2,
lambda = 1)
Parameters:
Value:
TypeFlag p
S 90
time1 0.5
Time2 1
r 0.06
b 0.06
sigma 0.2
lambda 1
Option Price:
9.582461
Description:
Tue Nov 13 20:02:02 2018
Title:
Partial Time Fixed Strike Lookback Option
Call:
PTFixedStrikeLookbackOption(TypeFlag = "c", S = 100, X = 90,
time1 = 0.5, Time2 = 1, r = 0.06, b = 0.06, sigma = 0.2)
Parameters:
Value:
TypeFlag c
S 100
X 90
time1 0.5
Time2 1
r 0.06
b 0.06
sigma 0.2
Option Price:
25.81262
Description:
Tue Nov 13 20:02:02 2018
Title:
Extreme Spread Option
Call:
ExtremeSpreadOption(TypeFlag = "c", S = 100, SMin = NA, SMax = 110,
time1 = 0.5, Time2 = 1, r = 0.1, b = 0.1, sigma = 0.3)
Parameters:
Value:
TypeFlag c
S 100
SMin <NA>
SMax 110
time1 0.5
Time2 1
r 0.1
b 0.1
sigma 0.3
Option Price:
10.46681
Description:
Tue Nov 13 20:02:02 2018
Title:
Extreme Spread Option
Call:
ExtremeSpreadOption(TypeFlag = "cr", S = 100, SMin = 90, SMax = NA,
time1 = 0.5, Time2 = 1, r = 0.1, b = 0.1, sigma = 0.3)
Parameters:
Value:
TypeFlag cr
S 100
SMin 90
SMax <NA>
time1 0.5
Time2 1
r 0.1
b 0.1
sigma 0.3
Option Price:
9.347113
Description:
Tue Nov 13 20:02:02 2018
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