Presentation is loading. Please wait.

# Multi-period BTM Dr. DAI Min.

## Presentation on theme: "Multi-period BTM Dr. DAI Min."— Presentation transcript:

Multi-period BTM Dr. DAI Min

Outline: Multi-period BTM
Vanilla options: European and American Barrier options Strongly-path dependent options: Asian, lookback Single-state variable BTM for some strongly-path dependent options Forward shooting grid method

Two-period BTM for vanilla options
Single-period BTM A local algorithm Two-period BTM Assumption: two-period tree

Multi-period BTM for vanilla options
S0u S0d S0u2 S0d2 S0u3 S0u4 S0d4 S0d3

A concise expression of BTM

With continuous dividend yield q

Multi-period BTM for American options
At any nodes of the tree, check if early exercise is optimal.

Barrier options Barrier options are triggered by the action of the underlying hitting a prescribed value at some time before expiry. Consider an up-out call: if the underlying price remains below the barrier level until maturity, the contract has a usual call payoff at expiry (red line). However, if the underlying reaches the level before expiry, then the option becomes worthless because it has ``knocked out'‘ (blue line).

Multi-period BTM for barrier options
Barrier options are weakly path-dependent

Strongly path-dependent options (I)
Strong path-dependent options: Asian options Lookback options Type of payoffs: Fixed strike Floating strike

Strongly path-dependent options (II)
Type of Asian payoffs Arithmetic average Geometric average

Strongly path-dependent options (III)
Type of lookback payoffs Maximum Minimum

BTM for Asian arithmetic options (I)

BTM for Asian arithmetic options (II)
A concise expression

BTM for lookback maximum

Single-state variable BTM for strongly path-dependent options (I)

Single-state variable BTM for strongly path-dependent options (II)

Single-state variable BTM for floating strike lookback put
A single-state variable tree:

Single-state variable BTM for floating strike Asian arithmetic
The single-state variable tree does not recombine! The amount of computation grows exponentially with the number of time steps.

Single-state variable BTM for American-style floating strike path-dependent options

Single-state variable BTM for fixed strike path-dependent options
For European case, a single-state variable BTM is available by a different transformation (Roger and Shi (1995)); For American case, not available.

Forward shooting grid method (FSGM)
Drawback of BTM For some path-dependent options, the number of tree nodes may grow exponentially with the number of time steps FSGM A local binomial model Implementation is confined to a lattice, instead of a tree. The number of nodes of the lattice does not grow exponentially. Single-state variable case General case Interpolation is needed in some scenarios.

Single-state variable FSGM for floating strike Asian arithmetic options

Two-state variable FSGM for arithmetic Asian options (I)

Two-state variable FSGM for arithmetic Asian options (II)

Two-state variable FSGM for lookback options
A similar procedure; No interpolation is required.

Download ppt "Multi-period BTM Dr. DAI Min."

Similar presentations

Ads by Google