top of page

 

​

​

DER 05.2 Arbitrage relations: Options

Call and put options on assets, forwards, futures, and swaps also trade. Certain price relations among these instruments exist solely due to the absence of costless arbitrage opportunities. The most important of these is called put-call parity.

​

  • Required reading

    • Whaley, 2006, Ch. 6, No-arbitrage price relations: Options

    • Whaley 2021, The "Sage" entrepreneur (teaching note)

​

​

​

DER 07 OPTION VALUATION: ANALYTICAL FORMULAS

Valuing an option relative to its underlying benchmark requires an assumption about the benchmark’s price distribution. Under the assumption that the benchmark’s price distribution is lognormally distributed, many valuation results may be derived. One such valuation result is the infamous Black-Scholes European-style option valuation formula.

​

​

​

​

OPTION VALUATION: BINOMIAL METHOD

Some options, because of their contract design, do not have analytical valuation formulas (e.g., American-style options). Nonetheless, they can be valued accurately using approximations. The most popular among these is the binomial method.

​

​

​

​

OPTION VALUATION: MONTE CARLO SIMULATION

Some options are written on the prices of more than one asset. Most of them do not have analytical valuation formula. Nonetheless, they can be valued accurately using approximations. The most versatile of these is Monte Carlo simulation.

​

​

​

​

RISK MEASUREMENT

The importance of option valuation is not driven solely by the desire to identify mispriced options. Its greatest value lies in providing managers with the ability to measure risk exposures.

​

​

​

​

MANAGING RISK DYNAMICALLY

With the ability to measure risk, we create the ability to manage risk through time.

​

  • Required reading

    • Whaley, 2006, Ch. 10, Risk management strategies: Options (pp. 347-362)

    • Saletta 20210128 What is a gamma squeeze? The Motley Fool.

​

​

​

EARNING EMBEDDED CONTRACT FEES

The terms of OTC contracts are often written in such a way that there is no obvious cost. The fees charged by the dealer are embedded. The embedded fees can be deduced using techniques such as Monte Carlo simulation.

​

​

  • Lecture notes

    • Slides

    • Supporting files​

      • Ted Turner collar valuation.xlsx

      • Earning embedded fee dynamically.xlsx

​

​

PASSIVE OPTION STRATEGIES

Passive option strategies are ones that are opened today and held to expiration. The expected returns/risks of these strategies can be computed straightforwardly using Monte Carlo simulation.

​

​

​

​

NOTE: All of the above ideas and techniques can be applied without identifying the specific nature of the asset underlying the derivatives contract. They are generic. In what lies below, we discuss how the ideas and techniques are applied to derivatives contracts written on specific assets.

​

STOCK INDEX FUTURES

The cost of carry model is adapted to the case where the underlying asset is a stock index like the S&P 500 index. Stock index futures are shown to be a cost-efficient and effective means of managing the risk of stock portfolios.

​

  • Required reading

    • Whaley, 2006 Ch. 14 Stock index products: Futures and options

    • Whaley, 2006 Ch. 15 Stock index products: Strategy-based

​

​

​

STOCK INDEX OPTIONS

Valuation models show how stock index options can be used to structure various types of index products such as protected equity notes and portfolio insurance.

​

  • Required reading

    • Whaley, 2006 Ch. 14 Stock index products: Futures and options

    • Whaley, 2006 Ch. 15 Stock index products: Strategy-based

    • Bollen and Whaley 2004 Does net buying pressure affect the shape of implied volatility functions? JF

​

​

 

STOCK DERIVATIVES

Futures and options on individual stocks are also traded on exchanges and in over-the-counter (OTC) markets, and lend themselves to various strategies such as capturing dividends and acquiring shareholder voting rights.

​

  • Required reading

    • Whaley, 2006, Ch. 11, Stock products

    • Frankel, 2012, Dividend play in S&P 500 ETF goes awry, costs traders $20 million

​

  • Lecture notes

    • Slides

    • Supporting files​

      • Early exercise of call.xlsx

​

​

COMPENSATION CONTRACTS

The most common OTC stock option contract category is executive stock options. Understanding how to value these contracts is critical in measuring the economic impact that they have on shareholder wealth.

​

​

​

​

​

bottom of page