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

Prices TreeProductAmerican for the seller. More...

#include <americanselleroptional.h>

Inheritance diagram for TreeProductAmericanSellerOptional:
TreeProductAmericanSeller TreeProductAmerican TreeProductRandomExercisable TreeProduct

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)

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>

Constructor & Destructor Documentation

TreeProductAmericanSellerOptional::TreeProductAmericanSellerOptional ( 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, 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.

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

Reimplemented from TreeProductAmericanSeller.


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