calibrate_kou: Calibrate the parameters of the Kou jump-diffusion model to...

In shill1729/OptionPricer: An option pricer for European and American vanilla stock options

Description

Calibrate the parameters of the Kou jump-diffusion model to market prices.

Usage

calibrate_kou(
  initial_guess,
  market,
  spot,
  maturity,
  rate,
  div,
  ku,
  kd,
  what,
  style,
  N,
  M,
  generate = FALSE,
  bounds = NULL
)

Arguments

initial_guess	initial guess of parameters, see details
market	market data, see details
spot	the underlying spot price
maturity	the option contract's maturity
rate	the risk-neutral rate
div	the dividend yield rate
ku	the upward jump displacement
kd	the downward jump displacement
what	what option to price
style	style of optionality: american or european
N	time resolution
M	space resolution
generate	whether to immediately generate a set of model prices
bounds	lower and upper bounds for parameters

Details

This is just a simple wrapper to R's base optim function for minimizing/maximizing functions of several parameters. We choose to fix the parameters: rate, div, ku, and kd and fit the model based on the remaining parameters. Calibrations tend to fail for deep OTM and moderately ITM options and no input handling is done in this function to prevent this, so it is up to the user to pass good data to this calibration routine. The objective function to minimize is merely the mean-square error between the market prices and the model prices. This is available explicitly as meansq_price_error_kou.

The input initial_guess should be a vector of 5 dimensions containing (not necessarily named)

• volat the annual volatility level

• lambda the mean rate of jumps per year

• prob the probability of upward jumps

• alpha the mean upward jump size

• beta the mean downward jump size

The input bounds should be a list containing, which may be set to NULL for default bounds

• lower the lower bounds of the parameters to calibrate

• upper the upper bounds of the parameters to calibrate

The input market should be a data.frame containing

• strike the strike price

• fee the market price

Value

Either a list from optim or a list containing

• market a list containing strike, fee and model

• fit the object returned from optim

shill1729/OptionPricer documentation built on June 11, 2020, 12:18 a.m.