John Merton Aldrich

Quant Corner Robert Merton Merton model for valuing corporate debt

‚robert merton, who’s best known for his academic work in developing option-pricing models, published his first scholarly paper on a topic far removed from finance: Gulliver’s Travels. While an undergraduate at Columbia University in New York, he wrote a piece for a literature class that analyzed the physical impossibility of a flying island as described in Jonathan Swift’s classic work. Merton...

Notes : Black - Scholes - Merton Model ( IEOR 4707 ,

denote an increment of the BM (with ds > 0). We also use N(μ, σ2) to denote a normal distribution with mean μ and variance σ2. Recall some of the key properties of BM: (i) B0 = 0; (ii) independent increments, i.e., dBs and dBt are independent, for any s + ds ≤ t; (iii) stationary increments, i.e., dBs follows a normal distribution N(0, ds). Note this last distribution depends only on the length...

Mathematical Models for Financial Management By MERTON

On Merton ́s Problem for Life Insurers

This paper deals with optimal investment and redistribution of the free reserves connected to life and pension insurance contracts in form of dividends and bonus. Formulated appropriately this problem can be viewed as a modification of Merton’s problem of optimal consumption and investment with a very particular form of consumption and utility hereof. Both are linked to a finite state Markov ch...

Introduction to Merton Jump Diffusion Model

This paper presents everything you need to know about Merton jump diffusion (we call it MJD) model. MJD model is one of the first beyond Black-Scholes model in the sense that it tries to capture the negative skewness and excess kurtosis of the log stock price density ( ) 0 ln( / ) T S S P by a simple addition of a compound Possion jump process. Introduction of this jump process adds three extra...