extract.rates: Extract Risk Free Rate and Dividend Yield
In RND: Risk Neutral Density Extraction Package

Description Usage Arguments Details Value Author(s) References Examples

extract.rates extracts the risk free rate and the dividend yield from European options.

1	extract.rates(calls, puts, s0, k, te)

`calls`	market calls (most expensive to cheapest)
`puts`	market puts (cheapest to most expensive)
`s0`	current asset value
`k`	strikes for the calls (smallest to largest)
`te`	time to expiration

The extraction is based on the put-call parity of the European options. Shimko (1993) - see below - shows that the slope and intercept of the regression of the calls minus puts onto the strikes contains the risk free and the dividend rates.

`risk.free.rate`	extracted risk free rate
`dividend.yield`	extracted dividend rate

Kam Hamidieh

D. Shimko (1993) Bounds of probability. Risk, 6, 33-47

#
# Create calls and puts based on BSM
#

r     = 0.05
te    = 60/365
s0    = 1000
k     = seq(from = 900, to = 1100, by = 25)
sigma = 0.25
y     = 0.01

bsm.obj = price.bsm.option(r =r, te = te, s0 = s0, k = k, sigma = sigma, y = y)

calls = bsm.obj$call
puts  = bsm.obj$put

#
# Extract rates should give the values of r and y above:
#

rates = extract.rates(calls = calls, puts = puts, k = k, s0 = s0, te = te)
rates