Stock Loan Valuation Under Brownian Motion-Based and Markov Chain Stock Models
Monday, June 11, 2018 - 2:00pm - 2:30pm
Stock loans involve two parties: a borrower and a lender. The borrower owns one share of stock and obtains a loan from the lender using the share of stock as collateral. At maturity, the borrower must choose between 1) repaying the lender the principal plus interest to regain the stock and 2) defaulting on the loan and surrendering the stock. Most classical work on stock loan valuation used Brownian motion-based stock models, but recently Markov chain models have gained in popularity. This talk presents stock loan valuation for a Markov chain model in which the price of the underlying stock is determined by a two-state Markov chain. Results are compared to stock loan valuation for classical Brownian motion-based stock models. Stock models that admit closed-form solutions for the stock loan value will be emphasized, and both American and European stock loans will be considered. Theoretical formulas and computational examples will be presented.