American-transaction costs 1.0.0.0
American option pricer under proportional transaction costs
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Prices TreeProductAmerican for the seller (deprecated). More...
#include <americanseller.h>
Public Member Functions | |
coefficient | current_price (const PiecewiseLinear ¤t, 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 ¤t_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 ¤t_hedge, const PiecewiseLinear &future_hedge, const coefficient x, coefficient &y, coefficient &S, const Portfolio &portfolio) const |
TreeProductAmericanSeller (const coefficient expiry, const PayoffBridge &payoff) |
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.
TreeProductAmericanSeller::TreeProductAmericanSeller | ( | const coefficient | expiry, |
const PayoffBridge & | payoff | ||
) | [inline] |
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
current | Lower boundary of set of hedging portfolios |
holdings | Current 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.
spot | Price of underlying asset |
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
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 |
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
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). |
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.
t | Current time |
spot | Price of underlying asset |
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 , and optionally numbers y and S in the bid-ask interval such that
.
Implements TreeProductRandomExercisable.
Reimplemented in TreeProductAmericanSellerOptional.