TreeProductAmericanSellerOptional Class Reference

Prices TreeProductAmerican for the seller. More...

#include <americanselleroptional.h>

Inheritance diagram for TreeProductAmericanSellerOptional:

List of all members.

Public Member Functions
coefficient	current_price (const PiecewiseLinear &current, const Portfolio &holdings=Portfolio(0, 0)) const
coefficient	expiry () const
PiecewiseLinear	final_hedge (const Spot &spot) const
PiecewiseLinear	interim_hedge (const coefficient time, const Spot &spot, const PiecewiseLinear &future_hedge) const
Portfolio	next_portfolio (const coefficient t, const Spot &spot, const PiecewiseLinear &future_hedge, const Portfolio &current_portfolio) const
Portfolio	payoff (const coefficient &t, const Spot &spot) const
PiecewiseLinear	payoff_hedge (const coefficient &t, const Spot &spot) const
coefficient	random_exercise (const coefficient t, const Spot &spot, const PiecewiseLinear &current_hedge, const PiecewiseLinear &future_hedge, const coefficient x, coefficient &y, coefficient &S, const Portfolio &portfolio) const
	TreeProductAmericanSellerOptional (const coefficient expiry, const PayoffBridge &payoff)

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Detailed Description

Prices TreeProductAmerican for the seller.

Allows for possibility that option may not be exercised at all, even if payoff at final time is non-zero.

Author:

Alet Roux <alet.roux@york.ac.uk>

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Constructor & Destructor Documentation

TreeProductAmericanSellerOptional::TreeProductAmericanSellerOptional	(	const coefficient	expiry,
		const PayoffBridge &	payoff
	)		[inline]

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Member Function Documentation

coefficient TreeProductAmericanSeller::current_price	(	const PiecewiseLinear &	current,
		const Portfolio &	holdings = Portfolio(0, 0)
	)		const [inline, virtual, inherited]

Computes current price of option, given the holdings of the investor

Parameters:

current	Lower boundary of set of hedging portfolios
holdings	Current holdings of investor

Implements TreeProduct.

coefficient TreeProduct::expiry

(

)

const [inline, inherited]

Expiry time.

PiecewiseLinear TreeProductAmericanSellerOptional::final_hedge

(

const Spot &

spot

)

const [inline, virtual]

Finds set of portfolios that hedges the option at its expiry time.

Parameters:

spot	Price of underlying asset

Returns:

Piecewise linear function that gives the lower boundary of set of hedging portfolios

Reimplemented from TreeProductAmericanSeller.

PiecewiseLinear TreeProductAmericanSeller::interim_hedge	(	const coefficient	t,
		const Spot &	spot,
		const PiecewiseLinear &	future_hedge
	)		const [inline, virtual, inherited]

Finds set of portfolios that hedges the payoff of the option at time t and in the future

Parameters:

t	Time
spot	Price of underlying asset
future_hedge	Piecewise linear function whose epigraph consist of portfolios that hedge the option at all future time steps

Returns:

Piecewise linear function that gives the lower boundary of set of hedging portfolios

Implements TreeProduct.

Portfolio TreeProduct::next_portfolio	(	const coefficient	t,
		const Spot &	spot,
		const PiecewiseLinear &	future_hedge,
		const Portfolio &	current_portfolio
	)		const [inline, inherited]

Given a portfolio that hedges at the current time, computes a portfolio into which the trader can enter that hedges at all future times

Parameters:

t	Time
spot	Price of underlying asset
future_hedge	Piecewise linear function whose epigraph consist of portfolios that hedge the option at all future time steps
current_portfolio	Current portfolio. Must correspond to a point in the epigraph of interim_hedge(t, spot, future_hedge) (this is not checked).

Returns:

Portfolio that will hedge the product over the next time step.

Portfolio TreeProductAmerican::payoff	(	const coefficient &	t,
		const Spot &	spot
	)		const [inline, inherited]

PiecewiseLinear TreeProductAmerican::payoff_hedge	(	const coefficient &	t,
		const Spot &	spot
	)		const [inline, inherited]

Finds set of portfolios that hedges the option at any time t before expiry.

Parameters:

t	Current time
spot	Price of underlying asset

Returns:

Piecewise linear function that gives the lower boundary of set of hedging portfolios

coefficient TreeProductAmericanSellerOptional::random_exercise	(	const coefficient	t,
		const Spot &	spot,
		const PiecewiseLinear &	current_hedge,
		const PiecewiseLinear &	future_hedge,
		const coefficient	x,
		coefficient &	y,
		coefficient &	S,
		const Portfolio &	portfolio
	)		const [inline, virtual]

Value of (least) optimal randomised stopping time for the buyer at time t with share price spot for the seller. The assumptions are that it has not been fully exercised yet, the current and future hedging portfolios are bounded from below by current_hedge and future_hedge, respectively, the number x is in the bid-ask interval, and shares is the current share holding. The function returns a number , and optionally numbers y and S in the bid-ask interval such that .

Reimplemented from TreeProductAmericanSeller.

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The documentation for this class was generated from the following file:

• treeproduct/americanselleroptional.h