Single Stock Option

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Single Stock Options Seminar
Part I Option Trading Overview By Steve D.
Chang Morgan Stanley Dean Witter Part II
Volatility Trading Concept and Application By
Charles Chiang Deutsche Bank A.G.
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Volatility Trading Concept and Application

• By Charles Chiang
• Vice President, GED Trading, Deutsche Bank

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Index

• Option Trading Strategies
• What Is Volatility?
• Volatility and Option Pricing
• Delta-Neutral Strategy
• Case Study 1
• Case Study 2
• Risks in Volatility Trading
• Application of Option Volatility Trading
• Option Risk Management
• Equity Derivative Structured Product
• Summary and Appendix (introduction on Deutsche
  Bank A.G.)

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Option Trading Strategy

• Leverage Trading / Directional Trading Strategy
• buy call, sell put, call spread, etc
• buy put, sell call, put spread, etc

Take a view on the market direction

• Volatility Trading Strategy

Take a view on the market volatility
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What Is Volatility?

• A measure of the degree of the fluctuations

• For example, compare the two listed companies in
  Taiwan
• TSMC (ticker 2330)
• Chung Hwa (ticker 2412)

Intuitively, which one do you think is more
volatile?
?
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What Is Volatility?
Volatility in statistical language

• Annual volatility

• Daily volatility

2330
2412
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Volatility and Option Pricing

• Option price is influenced by
• Underlying Stock Price
• Strike price
• Maturity
• Interest rate
• Dividend
• Volatility

• Assume that all the other factors are equal,
  will you pay the same price for the option
  written on TSMC and Chung Hwa?

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Volatility and Option Pricing

• The price of a call option increases when the
  underlying stock becomes more volatile.

• From buyers point of view, higher volatility
  means
• More chances to expire in the money
• From issuers point of view , higher volatility
  means
• Higher hedging cost

• Two types of volatility

• implied volatility
• actual volatility

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Delta-Neutral Strategy

• Delta

• Delta-neutral is the position where

• In a Delta-neutral position, small changes in
  stock price will not
• change the value of the stock-option
  portfolio.
• An example

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Case Study 1

• Buy 1,000 call option on TSMC. Assume that
• European style, expire in two months
• Sold at the money
• One option exchanged for one share
• Interest rate r2p.a.
• No dividend will be paid
• actual annual volatility sY 38.
• Sell underlying stock to keep the portfolio
  Delta-neutral by rehedging it from time to time.

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Case Study 1

• The benchmark for rehedging decision is sD
  2.4, which means

Daily change of stock price lt 2.4

Enjoy a leisure day
Daily change of stock price ? 2.4

Adjust the stock position to
achieve
Delta-neutral

• In our example, altogether there
• are 10 rehedges during the two-
• months life of the call option

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Case Study 1

• When sY38, 48 and 28, the outcomes of this
  strategy are

• When an investor buy an option whose implied
  volatility is lower than its actual one, he makes
  money no matter to which direction the market
  moves !

Fair Price
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Case Study 2

• Now consider buying 1,000 options on Chunghwa and
  short sell the underlying stock to hedge. Assume
  that all factors are the same as in the example
  of TSMC, except that actual annualised volatility
  is 25.
• when sY25, 35 and 15, the results are as
  followed

Fair Price
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Case Study 2

• Please note that the price for options written on
  Chung Hwa is relatively cheaper than that on TSMC
  (i.e. the former has a lower percentage price).

• This is because the volatility of TSMCs stock is
  higher than that of Chung Hwas.

Fair Price
Fair Price
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Risks in Volatility Trading

• Volatility trading strategy may be subjected to
  potential loss if the writer/buyer of option
  estimates the market volatility incorrectly.
• A single shock to stock price (e.g. 911 event,
  corporate action etc, whether positive or
  negative, may lead to great increase/decrease of
  the actual volatility of the underlying stock
• The daily up and down limit on underlying stock
  may obstruct timely rehedging and other friction
  in the underlying market (transaction cost,
  bid/offer spread, liquidity)
• Option model assumptions
• Regulatory risks such as foreign ownership limit,
  short selling restriction

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Application of Option Volatility Trading
(1) Option Risk Management

• Market makers usually reduce optionality risks by
  buying/selling options of same/different strike,
  maturity and hedge the net delta position between
  different options. For example
• Option portfolio may consist of three parts
• Short call with higher implied volatility(CH)
• Long call with lower implied volatility(CL)
• Long underlying stock
• The premium of CL eats up part of their profit
• When market volatility moves up unexpectedly, the
  profit in CL partially offset the loss in CH

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Application of Option Volatility Trading

• (1) Option Risk Management Examples

• Covered warrant risk management - buy short term
  single stock options to cover gamma risks in the
  the warrant book
• Index option volatility vs. single stock
  volatility - hedging or arbitrage between single
  stock volatility and index volatility
• CB volatility vs. single stock option volatility
  - take advantage on volatility differential
  between implied volatility from CB and single
  stock options

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Application of Option Volatility Trading

• One common example of equity derivative
  structured product is Equity Linked Note (ELN).
• Most popular examples are
• Principal Guaranteed Notes
• High Yield Notes (HYN)

• (2) Equity Derivative Structured Products

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Equity Derivative Structured Products

• Considerations U/L, participation, protected
  portion
• Structure Investor note options
• Pricing participation
• 
  (unprotected portion interest) /
  option value
• Types range / bull / bear

• Principle Guaranteed Notes

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Equity Derivative Structured Products
Principle Guaranteed Notes Example 1

• U/Ls TSMC
• Tenor 1/2 year on notes
• Options 100110 call spread
• Notes zero coupon note
• Protection 97
• Issue price 100
• Participation 100 of the appreciation of
  U/L on maturity
• Redemption on maturity, if
• appreciation of U/L lt 100, redemption will
  be 97
• 100 lt appreciation of U/L lt 110,
  redemption will be
• 97 appreciation of U/L
• appreciation of U/L gt 110, redemption
  will be
• 97 10

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Equity Derivative Structured Products
Principle Guaranteed Notes Example 2

• U/Ls TSMC
• Tenor 1/2 year on notes
• Options 100110 call spread
• Notes zero coupon note
• Protection 94
• Issue price 100
• Participation 100 of the appreciation of
  U/L on maturity
• Redemption on maturity, if
• appreciation of U/L lt 100, redemption will
  be 94
• 100 lt appreciation of U/L lt 110,
  redemption will be
• 94 appreciation of U/L
• appreciation of U/L gt 110, redemption
  will be 94 10

• The difference in protection rate above indicates
  a different implied volatility in the embedded
  call options

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Equity Derivative Structured Products
High Yield Notes

• Considerations U/L, issue price, annual yield
• Structure Investor note - options
• Pricing issue price PV(par) - option value
• Types bull / bear / range

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Equity Derivative Structured Products

• High Yield Notes Example

• U/Ls TSMC at 78.64
• Tenor 60 days on notes
• Options - 90 put, strike at 70.78
• Notes zero coupon note
• Issue price 98 of par
• Ann. Yield 12.2
• Redemption on maturity, if
• U/L close gt 90, redemption will be at 100
  of par
• U/L close lt 90, redemption will be the
  stock price on
• maturity / 70.78

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Summary

• Making profit without taking directional view but
  view on market volatility through delta-neutral
  strategy. (Provided that short selling facility
  on the underlying is possible)

Volatility trading concept and application

• Hedging option portfolio
• volatility risk (Gamma and Vega risk)
• liquidity risk (the discontinuous movement of
  stock price)

• Equity derivatives structured product
• combining equity options and fixed income
  securities whose feature depends on options
  premium paid/ sold