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

TreeProduct methods for American options More...

#include <american.h>

Inheritance diagram for TreeProductAmerican:
TreeProduct TreeProductAmericanBuyer TreeProductAmericanSeller TreeProductAmericanBuyerOptional TreeProductAmericanSellerOptional

List of all members.

Public Member Functions

virtual coefficient current_price (const PiecewiseLinear &current, const Portfolio &holdings=Portfolio(0, 0)) const =0
coefficient expiry () const
virtual PiecewiseLinear final_hedge (const Spot &spot) const =0
virtual PiecewiseLinear interim_hedge (const coefficient t, const Spot &spot, const PiecewiseLinear &future_hedge) const =0
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
 TreeProductAmerican (const coefficient expiry, const PayoffBridge &payoff)

Detailed Description

TreeProduct methods for American options


Constructor & Destructor Documentation

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

Member Function Documentation

virtual coefficient TreeProduct::current_price ( const PiecewiseLinear current,
const Portfolio holdings = Portfolio(0, 0) 
) const [pure 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

Implemented in TreeProductAmericanBuyer, TreeProductAmericanSeller, TreeProductEuropeanBuyer, and TreeProductEuropeanSeller.

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

Expiry time.

virtual PiecewiseLinear TreeProduct::final_hedge ( const Spot spot) const [pure virtual, inherited]

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

Implemented in TreeProductAmericanBuyer, TreeProductAmericanBuyerOptional, TreeProductAmericanSeller, TreeProductAmericanSellerOptional, TreeProductEuropeanBuyerOptional, TreeProductEuropeanSeller, and TreeProductEuropeanSellerOptional.

virtual PiecewiseLinear TreeProduct::interim_hedge ( const coefficient  t,
const Spot spot,
const PiecewiseLinear future_hedge 
) const [pure 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

Implemented in TreeProductAmericanBuyer, TreeProductAmericanSeller, and TreeProductEuropean.

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

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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