Potential Exchange Rate Range Using Currency Options Data
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This document discusses using implied volatility from currency options to estimate potential future ranges for exchange rates between the Indian rupee (INR) and US dollar (USD). It provides examples using real options data from June 22, 2012, June 25, 2012, and June 26, 2012 to calculate 1 standard deviation potential ranges for the INR-USD exchange rate with a 68% probability based on average straddle and strangle implied volatilities and annualization factors. The results estimate potential exchange rate ranges of 56.00-58.58 for June 27, 2012 and 54.08-60.98 for July 27, 2012 using the June 22 data.
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Potential Exchange Rate Range Using Currency Options Data
- 1. Potential range INR-USD Currency Options Data Sumantra Pal sumantrapal@gmail.com
- 2. 2.Can be ‘warning sign’ 3.Potential movements till expiry 4.Keep gazing at straddle and strangle Thoughts 5.IV: market “implies” future volatility based on option price Option price = f ( underlying, strikes, time to expiry, rfr, volatility) 6.volatility crash ‘events’ Ct = f (St, K, T - t, r, v) 7.dramatic changes in implied volatility Implied volatility 8.Play options + kill implied volatility v= g-1(C,.,.) 9.Cost effective than spot market interventions – Vega – responsiveness of option it doesn’t require dollars + leverage price w.r.t. implied volatility ∂C/∂v Test: if vega>0 always •if volatility is high, then option prices are high Derive vega-reciprocal ∂v/∂C and vice-versa. Test sign; •implied volatility estimate can be biased, if options traded are illiquid i.e. large Ask-bid if >0; sell options to kill v spreads If <0; buy options to kill v Jun/27/2012 sumantrapal@gmail.com 1of 5
- 3. 1. Import live data stream 2. Find the at-the-money straddle A crude method and out-of-the money strangle Option chain data 3. Pluck IVs for both and average straddle + strangle IV 4. (Futures price) x (IV) x sq.rt. Futures data, Premium/discount [days to expiration/ 365] = 1 Standard deviation 5. Potential range = Fut. ± with Potential range time series 68% probability Jun/27/2012 sumantrapal@gmail.com 2 of 5
- 4. Illustrations: Data at 17.00 on Jun/22/2012 Average IV of at-the-money straddle + out-of-the-money strangle: (14.26+11.05+13.40+10.66)/4=12.34|JUN Potential range (11.19+11.41+11.16+11.45)/4=11.30|JUL max OI call = 57.00, 56.00 max OI put = 57.00 Annualization factor 27th Jun Contract: √( 4/365) = 0.1047 IV range |JUN= 58.58 - 56.00 27th Jul Contract : √(34/365)= 0.3052 IV range |J UL = 60.98 - 54.08 1 standard deviation: 1.29|JUN , 3.45|JUL Futures |JUN = 57.29 Futures |JUL = 57.53 Potential range by: Futures |AUG = 57.83 27th Jun: 57.29 ± 1.29 = 58.58, 56.00 Futures |SEP = 58.03 27th Jul : 57.53 ± 3.45 = 60.98, 54.08 Premia > 0 Jun/27/2012 sumantrapal@gmail.com 3 of 5
- 5. Illustrations: Data at 17.00 on Jun/25/2012 Average IV of at-the-money straddle + out-of-the-money strangle: (14.18+10.25+11.82+10.79)/4=11.76|JUN Potential range (10.34+10.41+10.86+10.78)/4=10.60|JUL max OI call = 57.00, 56.00 max OI put = 57.00, 56.00 Annualization factor 27th Jun Contract: √( 2/365) = 0.0740 IV range |JUN= 57.93 - 56.19 27th Jul Contract : √(32/365)= 0.2961 IV range |J UL = 60.51- 54.23 1 standard deviation: Futures |JUN = 57.06 0.87|JUN , 3.14|JUL Futures |JUL = 57.37 Futures |AUG = 57.62 Potential range by: Futures |SEP = 57.89 27th Jun: 57.06 ± 0.87 = 57.93, 56.19 Premia > 0 27th Jul : 57.37 ± 3.14 = 60.51, 54.23 Jun/27/2012 sumantrapal@gmail.com 4 of 5
- 6. Illustrations: Data at 17.00 on Jun/26/2012 Average IV of at-the-money straddle + out-of-the-money strangle: (8.45+8.08+11.57+9.88)/4=9.495|JUN Potential range (10.30+10.50+11.84+11.64)/4=11.07|JUL max OI call = 57.00, 56.00 max OI put = 57.00, 56.00 Annualization factor 27th Jun Contract: √( 1/365) = 0.0523 IV range |JUN= 57.53 - 56.53 27th Jul Contract : √(31/365)= 0.2914 IV range |J UL = 60.54 - 54.08 1 standard deviation: Futures |JUN = 57.03 0.5|JUN , 3.23|JUL Futures |JUL = 57.31 Futures |AUG = 57.58 Potential range by: Futures |SEP = 57.84 27th Jun: 57.03 ± 0.5 = 57.53, 56.53 Premia > 0 27th Jul : 57.31 ± 3.23= 60.54, 54.08 Jun/27/2012 sumantrapal@gmail.com 5 of 5
- 7. 2.Rupee, Frequently Asked References Questions, Ajay Shah Blog 3.Liquidity considerations in es volatility, Rohini Grover and Susan Thomas Thank you
Editor's Notes
- Volatility is one of the important factors, which is taken into account while pricing options. It is a measure of the amount and the speed of price change. To estimate future volatility, a time-series analysis of historical volatility may be carried out to know the future movements of the underlying. Alternatively, one could work out implied volatility by entering all parameters into an option pricing model and then solving it for volatility. For example, the Black Scholes model solves for the fair price of the option by using the following parameters–days to expiry, strike price, spot price, and volatility of underlying, interest rate and dividend. This model could be used in reverse to arrive at implied volatility by putting the current price of the option prevailing in the market. Putting it simply implied volatility is the estimate of how volatile the underlying will be from the present until the expiry of option. If volatility is high, then the options premiums are relatively expensive and vice-versa. However, implied volatility estimate can be biased, especially if they are based upon options that are thinly traded samples. the option value, Ct, is usually defined as a function of five factors known as the direct determinants of an option value (Cox & Rubinstein, 1985): Ct = f (St, K, T - t, r, v) where St denotes the underlying asset price at time t, K the strike price, r the risk-free interest rate, T-t the time to maturity of the option, and the volatility of the underlying asset returns over the remaining life of the option. Of these direct determinants all except volatility are observable in the market.
- Volatility is one of the important factors, which is taken into account while pricing options. It is a measure of the amount and the speed of price change. To estimate future volatility, a time-series analysis of historical volatility may be carried out to know the future movements of the underlying. Alternatively, one could work out implied volatility by entering all parameters into an option pricing model and then solving it for volatility. For example, the Black Scholes model solves for the fair price of the option by using the following parameters–days to expiry, strike price, spot price, and volatility of underlying, interest rate and dividend. This model could be used in reverse to arrive at implied volatility by putting the current price of the option prevailing in the market. Putting it simply implied volatility is the estimate of how volatile the underlying will be from the present until the expiry of option. If volatility is high, then the options premiums are relatively expensive and vice-versa. However, implied volatility estimate can be biased, especially if they are based upon options that are thinly traded samples. the option value, Ct, is usually defined as a function of five factors known as the direct determinants of an option value (Cox & Rubinstein, 1985): Ct = f (St, K, T - t, r, ) where St denotes the underlying asset price at time t, K the strike price, r the risk-free interest rate, T-t the time to maturity of the option, and the volatility of the underlying asset returns over the remaining life of the option. Of these direct determinants all except volatility are observable in the market.