My Dissertation Report On
Using Interest Models to price CAPS and FLOORS

Submitted in partial fulfillment of the requirement of
Executive Masters in Business Administration (EMBA)

Area of Specialization
FINANCE


EXECUTIVE SUMMARY

Interest rate derivatives provide the means for controlling the risk of almost every financial transaction. In addition, interest rate derivatives may also be used to enhance the performance of investment portfolios. The interesting and crucial question is what are these instruments worth on the market and how can they be priced.

This thesis studies the three different pricing models namely The BDT Model, The HJM Model and The LIBOR Market Model.

The BDT model offers more flexibility. In case of constant volatility the expected yield of the Ho-Lee model moves exactly parallel, but the BDT model allows more complex changes in the yield-curve shape The ease of calibration to caps is one of the advantages in the case of the BDT model. The BDT model has two important disadvantages: (i) Inability to handle conditions where the impact of a second factor could be of relevance because of the one-factor model (ii) Inability to specify the volatility of yields of different maturities independently of future volatility of the short rate. An exact match of the volatilities of yields of different maturities should not be expected.

HJM model is a very general interest rate model, their only required inputs are the initial yield curve and the volatility structure for pure discount bond (PDB) price return. Here we provide the interest rate caps pricing model with very general volatility structure. When we test the valuation of interest rate derivatives in one-factor HJM model, we consider two different volatility structures as (i) exponentially decaying (ii) humped. We use Monte Carlo simulation combined with efficient bond return process and quasi-random sequences to price several interest rate derivatives included PDB option and caps. The result of this thesis is that we can price these interest rate derivatives accurately by Monte Carlo simulation combined with quasi-random sequences.

The LIBOR market model (LMM) is a tool for the pricing and hedging of interest rate derivatives. This paper presents the theory of the LMM and calibration along with practical issues arising while computer implementation.

Handwriting recognition

Abstract
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Handwriting recognition is the problem of transforming a word from the iconic form of writing to its symbolic form. The problem of handwriting script recognition has received attention from a number of researchers in the past. In this work, one application of Neural Network called Neocognitron is used. Fukushima’s Neocognitron [1-5] has received attention over the past two decades as a partially shift invariant, distortion tolerant classifier [3]. This is one of the most complex artificial neural network structures to simulate.
We have showed that using Neocognitron it is possible to make the machine to learn the general shape of a pattern and then use that to recognize the same pattern when it sees it again. In this paper, we have reviewed Fukushima’s work and the Neocognitron’s ability to recognize handwritten Arabic numerals, even with considerable deformations in shape, is demonstrated using a Windows platform.
We implemented the supervised version of the network following several of the papers written about the Neocognitron during the 1980s.The purpose of our implementation was mainly to understand the functionality of the Neocognitron, not to have a very efficient ‘work horse’. After reading the papers listed in the ‘References’ and ‘Bibliography’, we decided to implement a network similar in structure to the network mentioned in [3]. In that paper Fukushima supervises the network to recognize numerals. The reason to use similar topology as the one described in [3] was that the dimensions were explicitly stated. So we stayed with the original 4 stages (i.e. modules, S-C layer combinations). [4] Specifies most of the equations used for our network. This paper does not specify any dimensions for the network, but it has a precise mathematical appendix.
In the present paper, Neocognitron has been implemented in Windows platform and is shown to have a great capability for visual pattern recognition.

Handwriting recognition is the problem of transforming a word from the iconic form of writing to its symbolic form. The problem of handwriting script recognition has received attention from a number of researches in the past. In this work one application of Neural Network is used. Using Neocognitron it is possible to make the machine to learn the general shape of a pattern and then use that to recognize the same pattern when it sees it again.