Package 'empiricaloptions'

Build an empirical residual pool from a historical price series

Description

Fits a no-intercept AR(1) to first-differenced, discounted log-prices, then resamples the centered residuals with a stationary block bootstrap (Politis and Romano, 1994). The resulting pool is the reusable input to eq_price and eq_price_asian: build it once per discount rate and price as many strikes, maturities, and payoff types as needed from it.

Usage

eq_pool(prices, r, dt = 1/252, window = NULL, n_sims = 10000L, seed = 123)

Arguments

prices	Numeric vector of historical prices, ordered by date, with no missing values (interpolate or drop NAs beforehand).
r	Discount / funding rate (annualized, continuously compounded) used to discount prices into log-space before differencing.
dt	Time step between observations, in years (default 1/252 for daily data).
window	Optional trailing window length, in observations, to use instead of the full history (e.g. 252 for a trailing one-year window). NULL (default) uses the full series.
n_sims	Number of bootstrap paths to draw (default 10000).
seed	Random seed used for the bootstrap draw, for reproducibility.

Value

An object of class "eq_pool": a list with the resampled residual matrix (n_w rows by n_sims columns), the fitted AR(1) coefficient, and diagnostic statistics (Ljung-Box and ARCH-LM p-values on the pre-bootstrap residuals, annualized volatility, skew, and excess kurtosis).

References

Politis, D. N. and Romano, J. P. (1994). The stationary bootstrap. Journal of the American Statistical Association, 89(428), 1303-1313.

Examples

set.seed(1)
prices <- cumprod(1 + rnorm(500, 0.0003, 0.01)) * 100
pool <- eq_pool(prices, r = 0.03)
pool

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Price European options from an empirical residual pool

Description

Reconstructs terminal prices at maturity T by cumulating bootstrap residuals in log-space, applies a Duan-Simonato (1998) scalar martingale correction, and Monte Carlo-prices the requested strikes. Calls and puts are priced from the same simulated terminal draws, so put-call parity holds up to Monte Carlo noise by construction.

Usage

eq_price(pool, S0, T, K, type = c("call", "put"), eps_scale = 1)

Arguments

pool	An "eq_pool" object from eq_pool.
S0	Current (spot) price of the underlying.
T	Maturity, in years.
K	Numeric vector of strikes.
type	"call" or "put".
eps_scale	Optional scalar multiplier applied to the bootstrapped residuals before reconstruction (default 1); mainly a tool for sensitivity analysis, not needed in ordinary use.

Value

A list with components prices (named by strike), c_ds (the Duan-Simonato correction applied), and sigma_atm (the annualized at-the-money volatility implied by the simulated terminal distribution).

References

Duan, J.-C. and Simonato, J.-G. (1998). Empirical martingale simulation for asset prices. Management Science, 44(9), 1218-1233.

Examples

set.seed(1)
prices <- cumprod(1 + rnorm(500, 0.0003, 0.01)) * 100
pool <- eq_pool(prices, r = 0.03)
eq_price(pool, S0 = 100, T = 0.5, K = c(95, 100, 105), type = "call")

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Price arithmetic Asian call options from an empirical residual pool

Description

Extends eq_price to a path-dependent payoff by applying a date-specific Duan-Simonato correction at each fixing date, then averaging the corrected simulated path before applying the payoff. Requires no additional inputs beyond the pool already built for European pricing.

Usage

eq_price_asian(pool, S0, T, K, n_fix)

Arguments

pool	An "eq_pool" object from eq_pool.
S0	Current (spot) price of the underlying.
T	Maturity, in years.
K	Numeric vector of strikes.
n_fix	Number of (equally spaced) fixing/averaging dates up to T.

Value

Named numeric vector of arithmetic Asian call prices, one per strike.

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