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

Prices TreeProductAmerican for the seller (deprecated). More...

#include <americanseller.h>

Inheritance diagram for TreeProductAmericanSeller:
TreeProductAmerican TreeProductRandomExercisable TreeProduct 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
 TreeProductAmericanSeller (const coefficient expiry, const PayoffBridge &payoff)

Detailed Description

Prices TreeProductAmerican for the seller (deprecated).

Assumes that exercise at final time takes place whenever the final payoff of the option is nonzero, so may be faster for options with cash payoff.

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

Constructor & Destructor Documentation

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

Member Function Documentation

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

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.

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

Expiry time.

PiecewiseLinear TreeProductAmericanSeller::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

Implements TreeProduct.

Reimplemented in TreeProductAmericanSellerOptional.

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

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
coefficient TreeProductAmericanSeller::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 $\chi\in[0,1]$, and optionally numbers y and S in the bid-ask interval such that $x=\chi S + (1-\chi)y$.

Implements TreeProductRandomExercisable.

Reimplemented in TreeProductAmericanSellerOptional.


The documentation for this class was generated from the following file:
 All Classes Namespaces Files Functions Variables Typedefs Defines