American-transaction costs 1.0.0.0
American option pricer under proportional transaction costs
TreeProductAmericanBuyerOptional Class Reference

Prices TreeProductAmerican for the buyer. More...

#include <americanbuyeroptional.h>

Inheritance diagram for TreeProductAmericanBuyerOptional:
TreeProductAmericanBuyer TreeProductAmerican TreeProductExercisable TreeProduct

List of all members.

Public Member Functions

coefficient current_price (const PiecewiseLinear &current, const Portfolio &holdings=Portfolio(0, 0)) const
int exercise (const coefficient t, const Spot &spot, const Portfolio &current_portfolio) 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
 TreeProductAmericanBuyerOptional (const coefficient expiry, const PayoffBridge &payoff)

Detailed Description

Prices TreeProductAmerican for the buyer.

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>

Constructor & Destructor Documentation

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

Member Function Documentation

coefficient TreeProductAmericanBuyer::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:
currentLower boundary of set of hedging portfolios
holdingsCurrent holdings of investor

Implements TreeProduct.

int TreeProductAmericanBuyerOptional::exercise ( const coefficient  t,
const Spot spot,
const Portfolio current_portfolio 
) const [inline, virtual]

Is it optimal to exercise at this price and time?

Parameters:
tCurrent time
spotPrice of underlying asset
current_portfolioCurrent portfolio. Must correspond to a point in the epigraph of interim_hedge(t, spot, future_hedge).
Returns:
$ 1 $ if exercise is optimal and $ 0 $ if it isn't

Reimplemented from TreeProductAmericanBuyer.

coefficient TreeProduct::expiry ( ) const [inline, inherited]

Expiry time.

PiecewiseLinear TreeProductAmericanBuyerOptional::final_hedge ( const Spot spot) const [inline, virtual]

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

Parameters:
spotPrice of underlying asset
Returns:
Piecewise linear function that gives the lower boundary of set of hedging portfolios

Reimplemented from TreeProductAmericanBuyer.

PiecewiseLinear TreeProductAmericanBuyer::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:
tTime
spotPrice of underlying asset
future_hedgePiecewise 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:
tTime
spotPrice of underlying asset
future_hedgePiecewise linear function whose epigraph consist of portfolios that hedge the option at all future time steps
current_portfolioCurrent 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:
tCurrent time
spotPrice of underlying asset
Returns:
Piecewise linear function that gives the lower boundary of set of hedging portfolios

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