Valuation Of Swaption: Back To School

imagesContinuing with our last post on Swaption, we are here to discuss the “Valuation of Swaption” today. A swaption can be settled in 2 ways as :-

  1. Physical settlement:- when an option is exercised to go ahead with the underlying Interest rate swap; and
  2. Cash Settlement:- When an option is exercised for the cash value and the market value of the underlying swap changes hands upon exercise.

The valuation of Swaption is bit complicated and majorly depends on the 3 below mentioned situations-

  • AT-THE-MONEY:- When Strike Price = 0 “or” equals to the market rate
  • IN-THE-MONEY:- when Strike Price < 0 “or” less than the market rate (for the Payer Swaption)
  • OUT-OF-THE-MONEY:- When Strike Price > 0 “or” greater than the market rate (for payer swaption)

Quantitative analysts value swaption by constructing complex “lattice-based term structure” and “short rate models” that describe
the movement of interest rates over the time. However, A trader values European swaption using “the Black model“. For American and Bermudan styled options, where exercise is permitted prior to maturity, only the lattice based approach is applicable.

In lattice based approach, the analyst constructs a tree of short rates consistent with today’s yield curve and short rate volatility.
Then, Using this tree:
(1) the swap is valued at each node by “stepping backwards” through the tree, where at each node, its value is the discounted expected value of the up and down nodes. In the later time step, added to which is the discounted value of payments made during the time step in question, and noting that floating payments are based on the short rate at each tree-node. Then,
(2) the option is valued similar to the approach for equity options: at nodes in the time-step corresponding to option maturity, value is based on moneyness; at earlier nodes, it is the discounted expected value of the option at the up and down nodes in the later time step, and, depending on option style, of the swap value at the node. For both steps, the discounting is at the short rate at the tree-node in question.

In valuing European swaption using the Black model, the underlying swap is treated as a forward contract on a swap. The volatility is typically “read-off” a two dimensional grid of at-the-money volatility as observed from prices in the Interbank swaption market. On this grid, one axis is the time to expiration and the other is the length of the underlying swap.

The participants in the swaption market are predominantly large corporations, banks, financial institutions and hedge funds. End users such as corporations and banks typically use swaptions to manage interest rate risk arising from their core business or from their financing arrangements

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