Lecture 13

In Lecture 13, we studied the continuous-time limit of CRR stock prices. We rewrote stock prices in terms of log returns and used the central limit theorem to obtain lognormal stock-price distributions. We compared the real-world and risk-neutral formulas, which have different drifts but the same volatility.

Material used:

• Petters–Dong, Sec. 5.3.2, The Continuous-Time Security Price Formula, pp. 241–245.
• Supporting material: Sec. 5.2.1, The Real-World CRR Tree, pp. 219–230; Sec. 5.2.2, The Risk-Neutral CRR Tree, pp. 230–236; Sec. 5.3.1, The Lindeberg Central Limit Theorem, pp. 237–242.
• Formula sheet for Lecture 13

Remaining course schedule:

This week we have lectures only. There is no teaching on Thursday 29 October.

Two lectures remain: on 3 November, we will cover the Black–Scholes–Merton model and its pricing PDE; on 10 November, we will cover European call and put pricing formulas and put-call parity. Exercise sessions follow on 5 and 12 November.