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Utility Functions
George Fisher edited this page Feb 6, 2016
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library(ustreasuries)
#>
#> Attaching package: 'ustreasuries'
#> The following object is masked from 'package:stats':
#>
#> Gamma
- CAGR Calculate Compound Annual Growth Rates
PV <- 9000
FV <- 13000
years <- 3
# geometric
# =========
(geometric <- CAGR(9000, 13000, years, type="geometric"))
#> [1] 0.1304038
9000 * (1 + geometric) ** years
#> [1] 13000
# continuous
# ==========
(continuous <- CAGR(9000, 13000, years, type="continuous"))
#> [1] 0.1225749
9000 * exp(continuous * years)
#> [1] 13000
- r_continuous Convert from discrete to continuous
discrete <- 0.04
freq <- 2 # 4% compounded semi annually
(continuous <- r_continuous(discrete, freq))
#> [1] 0.03960525
- r_discrete Convert from continuous to discrete
PV <- 9000
FV <- 13000
years <- 3
freq <- 2 # compounding frequency = 2 => semi-annual
(continuous <- CAGR(PV, FV, years, type="continuous"))
#> [1] 0.1225749
(discrete <- r_discrete(continuous, freq))
#> [1] 0.126409
PV * (1 + discrete / freq) ** (freq * years)
#> [1] 13000
PV * exp(continuous * years)
#> [1] 13000
- discount_factor Calculate discount factor Z(t, T)
PV <- 9000
FV <- 13000
years <- 3
freq <- 2 # compounding frequency = 2 => semi-annual
(continuous <- CAGR(PV, FV, years, type="continuous"))
#> [1] 0.1225749
(discrete <- r_discrete(continuous, freq))
#> [1] 0.126409
(df_continuous <- discount_factor(continuous, years))
#> [1] 0.6923077
(df_discrete <- discount_factor(discrete, years, freq))
#> [1] 0.6923077
FV * df_continuous
#> [1] 9000
FV * df_discrete
#> [1] 9000
- CallParity Convert from a put-option price using put/call parity
- PutParity Convert from a call-option price using put/call parity
# Hull 7th edition Ch 17 P 357
Stock <- 49
Exercise <- 50
Time <- 20/52
Interest <- 0.05
Yield <- 0
sigma <- 0.20
EC = EuroCall(Stock, Exercise, Time, Interest, Yield, sigma)
EP = EuroPut(Stock, Exercise, Time, Interest, Yield, sigma)
PC = CallParity(Stock, Exercise, Time, Interest, Yield, EP)
PP = PutParity(Stock, Exercise, Time, Interest, Yield, EC)
writeLines(paste0("European Call Price:\t", EC, "\n",
"Call Parity Price:\t\t", PC, "\n",
"Difference:\t\t\t\t", EC-PC, "\n\n",
"European Put Price:\t", EP, "\n",
"Put Parity Price:\t\t", PP, "\n",
"Difference:\t\t\t\t ", EP-PP))
#> European Call Price: 2.40053407821637
#> Call Parity Price: 2.40053407821637
#> Difference: -7.105427357601e-15
#>
#> European Put Price: 2.44818219622651
#> Put Parity Price: 2.4481821962265
#> Difference: 3.5527136788005e-15
- RiskNeutralProb Binomial tree risk-neutral probability
Interest <- 0.05
Yield <- 0.10
sigma <- 0.20
deltaT <- 5
RiskNeutralProb(Interest, Yield, sigma, deltaT)
#> [1] 0.1507705
- ForwardPrice Forward price with or without income or yield
# Hull 7th edition Ch 5 P 103
# ===========================
Spot <- 40
Time <- 0.25
Interest <- 0.05
Yield <- 0
Income <- 0
ForwardPrice(Spot, Time, Interest, Yield, Income)
#> [1] 40.50314
# Hull 7th edition Ch 5 P 105
# ===========================
Spot <- 900
Time <- 0.75
Interest <- 0.04
Yield <- 0
Income <- 40 * exp(-0.03 * 4/12) # PV(40) = 39.60
ForwardPrice(Spot, Time, Interest, Yield, Income)
#> [1] 886.601
# Hull 7th edition Ch 5 P 107
# ===========================
Spot <- 25
Time <- 0.50
Interest <- 0.10
# convert 0.04 discrete to continuous
Yield_d <- 0.04
Yield <- r_continuous(Yield_d, 2)
Income <- 0
ForwardPrice(Spot, Time, Interest, Yield, Income)
#> [1] 25.76645
- ForwardRate Forward rate from Time1 to Time2 (discrete compounding)
- IntrinsicValueCall The in-the-money portion of a call option's premium
# Investopia: Intrinsic Value
# http://www.investopedia.com/terms/i/intrinsicvalue.asp
Stock <- 25 # S_0
Exercise <- 15 # K
IntrinsicValueCall(Stock, Exercise) # 10
#> [1] 10
- IntrinsicValuePut The in-the-money portion of a put option's premium
# Investopia: Intrinsic Value
# http://www.investopedia.com/terms/i/intrinsicvalue.asp
Stock <- 15 # S_0
Exercise <- 25 # K
IntrinsicValuePut(Stock, Exercise) # 10
#> [1] 10
- InTheMoneyCall Is a call option in the money?
# http://www.call-options.com/in-the-money.html
Stock <- 37.75 # S_0
Exercise <- 35 # K
InTheMoneyCall(Stock, Exercise) # TRUE
#> [1] TRUE
- InTheMoneyPut Is a put option in the money?
# http://www.call-options.com/in-the-money.html
Stock <- 35 # S_0
Exercise <- 37.50 # K
InTheMoneyPut(Stock, Exercise) # TRUE
#> [1] TRUE
See https://github.com/grfiv/BlackScholesMerton for these functions written in Python and Excel VBA
See also http://www.philadelphia-reflections.com/topic/230.htm