Monday, September 7, 2015

Option trading: Pricing and Volatility strategies and techniques - Euan Sinclair

Traders are pragmatic, interested in results. But focusing on the process can take care of the results. Good traders learn this. But good traders are intellectually parsimonious due to the demand of trading. But more knowledge brings more adaptability in uncertain times.

Derivatives traders don't need technical or fundamental analysis but sound knowledge of market structure and arbitrage relationships. Causality need to be investigated in every model.

Ch1. History

Options are not modern invention. They have a longer history than either stocks or bonds. Options are legal contracts, and hence subject to changes in the legal system (e.g. Dutch Tulips crash case in 1636). The South Sea bubble crash of 1720 involved a form of call options. The first exchange to list standardized contracts was the CBOE in 1973. Black-Scholes-Merton model published the same year. Options may well have been a tool in the speculative bubble, but were not the root cause. They are inevitable for modern risk management.  

Ch2. Introduction to Options

One must simply know  all details of the instrument's specifications. For example, FXP gives twice the daily negative returns of FXI, does not mean the compounded returns over a period of time will have the same relationship. Key words are: options, right not obligation, underlying, premium, maturity. Options can be created out of thin air, till there is ability to collateralize it. They have nonlinear payoffs. 

Specifications for an option contract

  1. Option type - calls and puts. 
  2. Underlying asset - certain number of stocks, indices (times a multiple), futures.
  3. Strike price - exercise price
  4. Expiration date - last date on which the option exists.
  5. Exercise style - American and European. Bermudan (on specific days).
  6. Contract unit - multiplier. Need to be aware of the effects of corporate actions. 

Uses of options

Replication of options using underlying is possible but expensive so options are not redundant. The subtle difference between the option and underlying replicating portfolio is where the professional traders make money.

  1. Hedging - A position in underlying can be protected from falls by buying a protective put. Presence of hedging activity shows the fallacy in methods that use the number of outstanding puts or calls to predict the direction of any underlying security.
  2. Speculation - If we think stocks will fall we can but a put. Out of money puts give greater leverage. 
  3. Creation of structured products - e.g. equity linked note. Investors are torn between fear and greed. Equity linked note are ideal product which promise principle and give an upside if the index is over a certain percentage.
  4. Volatility trading - A position in options and underlying can be used to trade change of volatility(and not directions or returns).
  5. Structured product arbitrage - Many financial products contain options like features, e.g. convertible bond. These can be replicated, hedge against or speculated using options.

Market structure

An options trade can be put with a broker after completing Securities account, options account and Options Clearing Corporation risk disclosure agreements. Market or Limit orders for Call or Put can be placed with details provided. Main exchanges in the US are Boston, Chicago Board, International Securities, NASDAQ Options, NYSE Alternext and Philadelphia. These markets are linked on a real-time basis. Ticks are either $0.05 or $0.01 generally in the US. There is also a private inter-dealer market called the 'call-around market'. The United States equity options market is served by a single clearing house, the Options Clearing Corporation (OCC), which the exchanges collectively own. The appropriate cash transfer happens the next business day. Transaction cost includes broker and exchange commissions. The margins are of two types - strategy based margin and portfolio based margin. 

Ch3. Arbitrage Bounds for Option Prices

Law of one price is behind these bounds. Sometimes what appears to be an arbitrage is merely a situation with larger than anticipated transaction costs, or unconsidered risk. The future price of a stock is related by $F=Se^{rT}$, where $r$ is the risk free rate. This is because of absence of arbitrage. A different borrowing and lending rate will give a no-arbitrage band instead of a value. Dividends and storage cost should be properly accommodated in the stock price. If interest rates are positively correlated with the underlying the futures are slightly more valuable than the forwards.

We can use this information to get bounds on options, which if violated can be exploited.

  1. American options are always expensive that European, both call and put. $c\le C$ and $p\le P$.
  2. A call can't cost more than underlying. $c\le S$.
  3. A put can never by more than the strike price (discounted to present for European). $P\le X$ and $p\le Xe^{-rt}$.
  4. The minimum value of call option is $c\ge S-Xe^{-rt}$. $C \ge Max(0,S-X)$.
  5. The minimum value of put option is $p \ge Xe^{-rt}-S$. $P \ge Max(0,X-S)$.

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