PROGRAMME ON CURRENCY OPTIONS
17-Aug-10
Anindya Banerjee
by
• What drives USD/INR.
• Introduction to FX options.
• Volatility and trading of volatility
• Options for directional trading
• Options for ranged markets.
• Arbitrage in NSE FX options.
• Neutralise directional bias
• Option sensitivity
CONTENTS
Factors affecting USD/INR
• Long term factors: Current Account situation and Capital accountflows.
Factors affecting USD/INR
Short-term Factors:
- Stock market.
- Risk aversion to emerging markets.
- Inter-relationship between USDINR and other Asian currencies.
- Inter-relationship between USDINR and global major currencies.
- RBI intervention.
• Option basics: Call & Put option, European option, strike price,money-ness or likelihood of expiring “in the money”, expiry date, delivery date, futures price.
• Option price /premium = Intrinsic value (tangible)+ extrinsic value (expected).
USD/INR call option of August 2010, strike 46, trading @ 0.58 INR. Forward rate is 46.37.
Option premium (0.58) = Intrinsic Value (0.37)+ Extrinsic Value (0.21).
• Factors that drive an option price:
Price of USD/INR, Time to expiration, Volatility, Interest rate differential, Intrinsic Value.
• Buyer bets on small probability of large move, Seller bets on large probability of small move
INTRODUCTION
1. The distribution of terminal currency exchange rate (returns) is lognormal.
2. There are no arbitrage possibilities.
3. Transactions cost and taxes are zero.
4. The risk-free interest rates, the foreign interest rates, and the exchange rate volatility are known functions of time over the life of the option.
5. There are no penalties for short sales of currencies.
6. The market operates continuously and the exchange rates follows a continuous Ito process.
GARMAN KOHLHAGEN MODEL
PROFITING FROM VOLATILITY…involves figuring out whether or not the price will hit the
Strike, and in how much time
ON VOLATILITY
• Volatility = Sudden-ness + Size of currency movements.
• Two types of Volatility: Historical and Implied
• Historicals are calculated statistically from historical prices
Exist largely in theory, seldom used in practice.
Lagging indicator
• Implieds are back-calculated from the prevailing option prices and fed back to get new prices. Are leading indicator, reflect market’s anticipation of future movement.
Close correlation between Spot
(underlying) and Vols.
Vols fall alongwith fall in Spot
Vols rise alongwith rise in Spot
Falls in Spot have been gradual.
Rise in Spot has been sudden. This
is reflected in the Volatility.
Correlation between Spot and Vols
6
8
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23-D
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44
45
46
47
48
49
50
51
52
53
3M Vol
USDINR Close
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Correlation between Spot and Vols
6
8
10
12
14
16
18
20
23-D
ec-0
8
28-J
an-0
9
25-F
eb-0
9
26-M
ar-
09
23-A
pr-
09
25-M
ay-0
9
23-J
un-0
9
21-J
ul-09
19-A
ug-0
9
18-S
ep-0
9
19-O
ct-
09
17-N
ov-0
9
15-D
ec-0
9
15-J
an-1
0
16-F
eb-1
0
19-M
ar-
10
20-A
pr-
10
19-M
ay-1
0
17-J
un-1
0
15-J
ul-10
13-A
ug-1
0
44
45
46
47
48
49
50
51
52
53
3M Vol
USDINR Close
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MAKING MONEY FROM VOLS
BASICBuy / Sell Call / Put Strike I / A / O Cost
Buy Call 46.34 ATM 3796
Buy Put 46.34 ATM 3796
Total Cost 7592
Underlying View Volatile, in either directon
Max Risk Limited to Cost paid
Max Return Limited after a point
Characteristic 2 legged option
Name Straddle
MAKING MONEY FROM VOLS
INTERMEDIATEBuy / Sell Call / Put Strike I / A / O Cost
Buy Call 46.34 ATM 3796
Buy Call 46.8 OTM 2102
Sell Call 46.00 ITM -5684
Total cost 214
Underlying View Volatile with an upward bias
Max Risk Limited
Max Return Unlimited on the upside
Characteristic leveraged
Name Short Call Ladder
PROFITING FROM DIRECTIONAL BETS…
Hoping your view is right, not really losing if it is not!
PROFITING FROM DIRECTIONAL BETS
BASICBuy / Sell Call / Put Strike I / A / O Cost
Buy Call 46.34 ATM 3796
Underlying View Bullish on USDINR
Max Risk Limited to Cost paid
Max Return Unlimited
Characteristic One single option
Name As Plain Vanilla as they come
PROFITING FROM DIRECTIONAL BETS
INTERMEDIATEBuy / Sell Call / Put Strike I / A / O Cost
Buy Call 46.34 ATM 3796
Sell Call 47.34 OTM -559
Total Cost 3237
Underlying View Bullish, but only upto a point
Max Risk Limited to Cost paid
Max Return Limited after a point
Characteristic 2 legged option
Name Bull Spread
PROFITING FROM DIRECTIONAL BETS
ADVANCEDBuy / Sell Call / Put Strike I / A / O Cost
Sell Put 46.50 ITM -4165
Buy Put 46.00 OTM 4628
Total Cost 463
Underlying View Large downmove.
Max Risk Limited
Max Return Unlimited on the downside
Characteristic Leveraged, 1X2
Name Put Back Spread
PROFITING FROM RANGED MARKETS…
Make money when no one else can
PROFITING IN RANGED MARKETS
PROFITING IN RANGED MARKETS
BASICBuy / Sell Call / Put Strike I / A / O Cost
Sell Call 47.00 OTM -1014
Sell Put 45.68 OTM -970
Total Cost -1984
Underlying View Ranged market
Max Risk Unlimited
Max Return Limited to premium collected
Characteristic 2 legged option
Name Strangle
PROFITING IN RANGED MARKETS
INTERMEDIATEBuy / Sell Call / Put Strike I / A / O Cost
Sell Call 46.40 OTM -3289
Buy Call 46.75 OTM 2145
Sell Put 46.00 OTM -1891
Buy Put 45.50 OTM 1072
Total cost -1963
Underlying View Ranged market
Max Risk large but limited
Max Return Limited to premium collected
Characteristic 4 Legged option
Name Iron Condor
PROFITING IN RANGED MARKETS
ADVANCEDBuy / Sell Call / Put Strike I / A / O Cost
Buy Call 46.00 ITM 5684
Sell Call 46.76 OTM -1671
Sell Call 46.76 OTM -1671
Total cost 2342
Underlying View Ranged with bearish bias
Max Risk Unlimited
Max Return More than premium collected
Characteristic leveraged 1x2
Name Call Ratio Spread
ARBITRAGE: RISKLESS PROFITS
• Arbitrage relates to taking advantage of mis-pricing in USD/INR options. Frequency of mis-pricing is high in markets where liquidity is still not abundant. Even liquid option markets like NSE equity options do exhibit mis-pricing from time to time.
• How to capitalise on mis-pricing of options?
- Triangle strategy: based on put-call parity.
• Triangle strategy: Suppose…
USD/INR 46.00 Aug Call is quoting 0.64.
USD/INR 46.00 Aug Put is quoting 0.24
USD/INR Futures for Aug is quoting 46.34
Difference between Call and Put premium = INR 0.40
No arbitrage spread level = (46.34-46.00)= INR 0.34
Risk-less profit = INR ((0.40-0.34)*1,000,000)= INR 60,000.
• Trade: Sell 46 Aug Call, buy 46 Aug Put, Buy USD/INR futures. Qty= 1 million USD.
ARBITRAGE: RISKLESS PROFITS
• Box Spread: Bull-bear spread trade.
• Box spread strategy: Suppose…USD/INR 46.00 Aug Call is quoting 0.40USD/INR 46.50 Aug call is quoting 0.20USD/INR Futures for Aug is quoting 46USD/INR 46.00 Aug Put is quoting 0.38USD/INR 46.5 Aug Put is quoting 0.78Cost of a bull spread 46/46.5 = INR 0.2Cost of bear spread 46/46.5 = INR 0.4Total cost of the bull and bear spread = INR 0.6No arbitrage cost should have been = (46.5-46.00)= INR 0.5Risk-less profit = INR ((0.6-0.5)*1,000,000)= INR 1,00,000.
• Trade: Sell 46 Aug Call, buy 46.5 Aug call, Buy 46 Aug put and sell 46.5 Aug put
• Qty= 1 million USD.
CAN I MAKE MONEY WITHOUT BETTING ON DIRECTION?
• How to be neutral on direction?
Hedge the delta on your option portfolio.
• How to hedge delta of option portfolio?
Portfolio:
Long 10 contracts of 46 August put @ 2062.56. Delta = (-) USD 3540.
In order to neutralise delta, we have to buy 3540 USD @ 46.20.
Post delta hedging the option portfolio is for the moment would not be affected from a upward or downward movement in the USD/INR.
• When do we make our portfolio delta neutral?
- When we are looking to trade other Greeks viz., Gamma, Theta, Vega.
- Want to minimize directional impact on portfolio.
• Option gives us the flexibility of making money without having to always bet on market direction.
Delta is change in Option Price due to change in Spot. It is not exactly, but is taken to be the chance of the Option expiring In the Money
OPTION GREEKS
• What are option Greeks?
Option Greeks are set of factor sensitivities used for measuringrisk exposures related to options.
• Delta, Gamma, Theta, Vega, Rho.
KEY INTER-RELATIONS
BETWEEN GREEKS
• Delta vs. money-ness (ATM, ITM or OTM) : In the money options (ITM) have higher delta than out of the money options (OTM).
• Gamma, Vega & theta vs. money-ness : At the money options have the highest Gamma, Theta and Vega. All three decline as theoption moves in or out of money.
• Gamma vs. Time : Gamma increases as time to expiry declines.
• Theta vs. Time : Theta increases as time to expiry declines.
• Vega vs. Time : Vega decreases as time to expiry declines.
• Delta vs. Volatility: Delta of an ITM declines and OTM increases.
http://montegodata.co.uk/Consult/Garman/garman.htm
PROGRAMME ON CURRENCY OPTIONS
17-Aug-10
Thank You!www.kshitij.com
033-24892010 /12
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