In grfiv/ustreasuries: Treasury Data Download, Fixed-Income Models and Derivative Analyses

knitr::opts_chunk$set(collapse=TRUE,                # hadley
                      comment = "#>",               # hadley
                      error=TRUE, purl=FALSE,       # to be able to see errors
                      fig.width=7.25, fig.height=6) # nice-sized pictures

library(ustreasuries)

• CAGR Calculate Compound Annual Growth Rates

PV    <- 9000
FV    <- 13000
years <- 3

# geometric
# =========
(geometric  <- CAGR(9000, 13000, years, type="geometric"))
9000 * (1 + geometric) ** years

# continuous
# ==========
(continuous <- CAGR(9000, 13000, years, type="continuous"))
9000 * exp(continuous * years)

• r_continuous Convert from discrete to continuous

discrete <- 0.04
freq     <- 2     # 4% compounded semi annually

(continuous <- r_continuous(discrete, freq))

• 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"))
(discrete   <- r_discrete(continuous, freq))

PV * (1 + discrete / freq) ** (freq * years)

PV * exp(continuous * years)

• 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"))
(discrete   <- r_discrete(continuous, freq))

(df_continuous <- discount_factor(continuous,  years))

(df_discrete   <- discount_factor(discrete,  years, freq))

FV * df_continuous
FV * df_discrete

all.equal(df_continuous, df_discrete) # df_continuous == df_discrete

• 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))

• RiskNeutralProb Binomial tree risk-neutral probability

Interest <- 0.05
Yield    <- 0.10
sigma    <- 0.20
deltaT   <- 5
RiskNeutralProb(Interest, Yield, sigma, deltaT)

• 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)

# 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)

# 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)

• 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

• 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

• 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

• 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

grfiv/ustreasuries documentation built on May 17, 2019, 8:36 a.m.