In the accrual swap discussed in the text, the fixed side...

Name: Problem 7, Chapter 34: Options, Futures, and Other Derivatives
Uploaded: 2020-02-18T18:01:05-08:00
Duration: 4 min 1 s
Channel: Alexander Allen
Description: In the accrual swap discussed in the text, the fixed side accrues only when the floating reference rate lies below a certain level. Discuss how the analysis can be extended to cope with a situation where the fixed side accrues only when the floating reference rate is above one level and below another.

In the accrual swap discussed in the text, the fixed side accrues only when the floating reference rate lies below a certain level. Discuss how the analysis can be extended to cope with a situation where the fixed side accrues only when the floating reference rate is above one level and below another.

Key Concepts

Accrual Swaps

An accrual swap is a type of interest rate swap where the payments on one or both sides accrue only when certain conditions are met regarding the underlying rate. This conditional accrual element introduces optionality to the payoff structure, blending characteristics of swaps with those of options.

Conditional Accrual Mechanism

This mechanism sets specific conditions under which interest accrues, such as the underlying rate being above or below a certain barrier. It is a key feature in structuring derivatives where payments depend on the performance or level of a reference rate, making the payoff contingent on realized rates.

Range Accrual Feature

Extending the conditional accrual concept, a range accrual feature requires the reference rate to lie within a predefined range for accrual to occur. This adds complexity to the derivative as the payment depends on the rate remaining within both a lower and an upper boundary, enhancing the product's sensitivity to rate movements.

Valuation Techniques for Exotic Derivatives

Valuing instruments with conditional and range accrual features typically requires advanced methodologies such as simulation-based approaches (e.g., Monte Carlo methods), analytical approximations, or solutions to partial differential equations. These techniques accommodate the path-dependent and non-linear payoff characteristics introduced by the accrual conditions.

Transcript

00:01 We have a situation with wood floating in water.

00:08 We have a tank with a piece of wood suspended by a cable, a string.

00:23 The tension force here.

00:26 And what happens is the string breaks and of course the wood rises to the surface.

00:48 So the question asks us, suppose the flask with the wood tied to the bottom is placed on a scale.

00:58 At some point the string breaks the wood rises to the surface where it floats.

01:02 When the wood is floating is the reading on the scale greater than, less than, or equal to the previous reading? and then choose the corresponding explanation.

01:13 This is rather a misunderstanding of forces to assume that anything dramatic is going on here.

01:21 For example, you can consider the tension in the rope being equal to the buoyancy force, subtract the force of gravity.

01:34 This course is equal to the density of the water, volume of the displaced water, times g subtract of mg here.

01:52 So what's going on is we've got this additional upwards force agreed.

01:56 Yes, there is.

01:59 Suddenly the thing rises to the top.

02:02 The force of buoyancy is taken over.

02:05 But before that, the greatest submersion was locked up in the tension.

02:11 There's where the force was.

02:12 So everything equals out...