Reference (apr02) Single Stock Option’s Seminar Part I Option Trading Overview By Steve D. Chang Morgan Stanley Dean Witter Part II Volatility Trading.

Reference (apr02)

Single Stock Option’s 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.

Reference (apr02)

Volatility Trading Concept and Application

By Charles ChiangVice 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

Take a view on the market volatility

Volatility Trading Strategy

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What Is Volatility?

A measure of the degree of the fluctuations

Intuitively, which one do you think is more volatile?

For example, compare the two listed companies in Taiwan

– TSMC (ticker: 2330)

– Chung Hwa (ticker: 2412)

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– Daily volatility

What Is Volatility?

N

iiY rr

NT 1

2)(1

11– Annual volatility

days trading annualYD /

2330 2412

DateLast Price

Daily Return Date

Last Price

Daily Return Date

Last Price

Daily Return

10-May 51.5 -0.98% 31-May 53.5 -0.94% 21-Jun 53 0.00%13-May 51 0.98% 3-Jun 53 -1.90% 24-Jun 53 2.79%14-May 51.5 0.00% 4-Jun 52 0.96% 25-Jun 54.5 0.00%15-May 51.5 -0.98% 5-Jun 52.5 0.00% 26-Jun 54.5 0.91%16-May 51 -0.99% 6-Jun 52.5 0.95% 27-Jun 55 -1.83%17-May 50.5 -1.00% 7-Jun 53 -0.95% 28-Jun 54 -1.87%20-May 50 0.00% 10-Jun 52.5 0.00% 1-Jul 53 1.87%21-May 50 1.00% 11-Jun 52.5 3.74% 2-Jul 54 0.92%22-May 50.5 0.00% 12-Jun 54.5 0.91% 3-Jul 54.5 -0.92%23-May 50.5 0.99% 13-Jun 55 -2.77% 4-Jul 54 -0.93%24-May 51 1.94% 14-Jun 53.5 0.00% 5-Jul 53.5 0.00%27-May 52 -1.94% 17-Jun 53.5 0.00% 8-Jul 53.5 2.77%28-May 51 4.79% 18-Jun 53.5 -0.94% 9-Jul 55 -0.91%29-May 53.5 1.85% 19-Jun 53 -0.95% 10-Jul 54.530-May 54.5 -1.85% 20-Jun 52.5 0.95% 0.13%Average Return

%4.2%38 DY %6.1%25 DY

DateLast Price

Daily Return Date

Last Price

Daily Return Date

Last Price

Daily Return

10-May 78.6 -1.76% 31-May 77.73 -0.59% 21-Jun 69 -0.73%13-May 77.3 2.33% 3-Jun 77.27 -4.20% 24-Jun 68.5 1.45%14-May 79.1 3.39% 4-Jun 74.09 0.62% 25-Jun 69.5 -4.41%15-May 81.8 -1.69% 5-Jun 74.55 -1.85% 26-Jun 66.5 0.00%16-May 80.5 1.12% 6-Jun 73.18 -7.08% 27-Jun 66.5 2.23%17-May 81.4 -2.83% 7-Jun 68.18 0.00% 28-Jun 68 -1.48%20-May 79.1 -0.57% 10-Jun 68.18 -1.34% 1-Jul 67 -1.50%21-May 78.6 1.71% 11-Jun 67.27 -2.74% 2-Jul 66 -3.86%22-May 80 -1.14% 12-Jun 65.45 4.76% 3-Jul 63.5 1.56%23-May 79.1 0.58% 13-Jun 68.64 0.00% 4-Jul 64.5 3.80%24-May 79.6 -1.15% 14-Jun 68.64 -2.02% 5-Jul 67 5.80%27-May 78.6 -0.59% 17-Jun 67.27 2.02% 8-Jul 71 0.70%28-May 78.2 -0.58% 18-Jun 68.64 -0.20% 9-Jul 71.5 -2.12%29-May 77.7 1.16% 19-Jun 68.5 0.00% 10-Jul 7030-May 78.6 -1.16% 20-Jun 68.5 0.73% -0.27%Average Return

Volatility in statistical language

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

Actual Volatility

Option PricingModel

Fair Value of Option

Implied Volatility

Option PricingModel

Market Value of Option

– 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 price stockof change

price option of changeDelta

Deltacall in position long

stockin position short

DATE 20/05/2002Stock price Option Price Delta Long call Short stock

79.09 5.42 0.6011 1000 -601

Stock Price chg. of stock price Option Price chg. of portfolio79.485 0.50% 5.66 -0.01%79.881 1.00% 5.91 -0.03%80.276 1.50% 6.16 -0.06%79.09 0.00% 5.42 0.00%

78.695 -0.50% 5.19 -0.01%78.299 -1.00% 4.96 -0.03%77.904 -1.50% 4.73 -0.06%

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

-1.00%

-0.50%

0.00%

0.50%

-2.00% -1.00% 0.00% 1.00% 2.00%

chg. of portfolio value

chg. of share price

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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 r=2%p.a.;

– No dividend will be paid;

– actual annual volatility σY= 38%.

Sell underlying stock to keep the portfolio Delta-neutral by rehedging it from time to time.


Case Study 1

The benchmark for rehedging decision is σD= 2.4%, which means

Daily change of stock price < 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

-10.00%

-5.00%

0.00%

5.00%

10.00%


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 !

Case Study 1

When σY=38%, 48% and 28%, the outcomes of this strategy are: Fair Price

38% 48% 28%$ 4.99 6.27 3.72% of stock price on the day of issuance 6.35% 7.97% 4.73%

-4,992.98 -6,268.19 -3,715.915,013.88 5,734.95 4,108.06

0.00 0.00 0.0020.90 -533.24 392.15Total P/L

Price of Call Option

Implied Volatility

Call Option Premium PaidP/L on Stock Hedging PositionExpiring Value of Call Options


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 σY=25%, 35% and 15%, the results are as followed:


-2,182.42 -3,019.03 -1,345.37-785.60 -1,646.68 -1,027.83

3,000.00 3,000.00 3,000.0031.98 -1,665.71 626.80

Expiring Value of Call OptionsTotal P/L

Implied Volatility

Price ofCall Option

Call Option Premium PaidP/L on Stock Hedging Position

Fair Price


This is because the volatility of TSMC’s stock is higher than that of Chung Hwa’s.

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).

Fair Price


-4,992.98 -6,268.19 -3,715.915,013.88 5,734.95 4,108.06

0.00 0.00 0.0020.90 -533.24 392.15Total P/L

Price of A Call Option

Implied Volatility

Cost of Call OptionsP/L on Stock PositionExpiring Value of Call Options


-2,182.42 -3,019.03 -1,345.37-786.50 -1,646.68 -1,027.83

3,000.00 3,000.00 3,000.0031.08 -1,665.71 626.80

Expiring Value of Call OptionsTotal P/L

Implied Volatility

Price of A Call Option

Cost of Call OptionsP/L on Stock Position

Fair Price


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



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

(1) Option Risk Management


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


(1) Option Risk Management — Examples


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

BondEquity

Derivatives+ =

Structure:Bull/Bear/RangeUnderlying:Stock/Basket/Index

Return:Coupon/Redemption(fixed or dependent on underlying performance)

Equity Linked Note


Considerations: U/L, participation, protected portion

Structure: Investor + note + options

Pricing: participation =

(unprotected portion + interest) / option value

Types: range / bull / bear

Principle Guaranteed Notes

Equity Derivative Structured Products



U/Ls: TSMCTenor: 1/2 year on notesOptions: + 100~110 call spread Notes: + zero coupon noteProtection: 97%Issue price: 100% Participation: 100% of the appreciation of U/L on maturity

Redemption: on maturity, if * appreciation of U/L < 100%, redemption will be 97%* 100% <= appreciation of U/L < 110%, redemption will be 97% + appreciation of U/L * appreciation of U/L >= 110%, redemption will be 97% + 10%

Principle Guaranteed Notes — Example 1



U/Ls: TSMCTenor: 1/2 year on notesOptions: + 100~110 call spread Notes: + zero coupon noteProtection: 94%Issue price: 100% Participation: 100% of the appreciation of U/L on maturity

Redemption: on maturity, if * appreciation of U/L < 100%, redemption will be 94%* 100% <= appreciation of U/L < 110%, redemption will be 94% + appreciation of U/L * appreciation of U/L >= 110%, redemption will be 94% + 10%

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

Principle Guaranteed Notes — Example 2



Considerations: U/L, issue price, annual yield

Structure: Investor + note - options

Pricing: issue price = PV(par) - option value

Types: bull / bear / range

High Yield Notes



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 >= 90%, redemption will be at 100% of par

* U/L close < 90%, redemption will be the stock price on

maturity / $70.78

High Yield Notes — Example


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

Reference (apr02) Single Stock Option’s Seminar Part I Option Trading Overview By Steve D. Chang Morgan Stanley Dean Witter Part II Volatility Trading.

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