American-transaction costs 1.0.0.0
American option pricer under proportional transaction costs
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Prices TreeProductAmerican for the seller. More...
#include <americanselleroptional.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 |
TreeProductAmericanSellerOptional (const coefficient expiry, const PayoffBridge &payoff) |
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.
TreeProductAmericanSellerOptional::TreeProductAmericanSellerOptional | ( | const coefficient | expiry, |
const PayoffBridge & | payoff | ||
) | [inline] |
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
current | Lower boundary of set of hedging portfolios |
holdings | Current 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.
spot | Price of underlying asset |
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
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 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 , and optionally numbers y and S in the bid-ask interval such that
.
Reimplemented from TreeProductAmericanSeller.