Options, Futures and Risk Management - BHP Company - Case Study Example

TOPIC: OPTIONS, FUTURES AND RISK MANAGEMENT REPORT By student’s Name: Code+ Course: Instructor’s Name: University Name: City, State: Date of submission: Executive Summary The report delved into the rationale for mispriced options by Black- Scholes Option Pricing Model. The model assumes constant volatility and that is the main reason as to why it misprices option contracts. The report relied on the statistics from BHP Company as from 16th September to 4th October 2013 and the aim was to compute implied volatility. The report sought to compare the implied volatility computed from the real option price with the model’s assumed volatility. The report found that there was under-pricing on the Out-of-The-Money options and the In- the- Money Options were overpriced due to the erroneous hypothesis on the volatility. The report also ascertains that the model usually misprices options in the short term as the size of erroneous volatility estimation reduce as the time taken to mature increases. The report indicates how the options are mispriced by the model, how, In –the – Money Options are under-priced by the model and how the model over prices the Out-of-Money-Options thus mispricing of the call option. The report made use of information from the options traded between 16th September to 4th October for three weeks. The data was from BHP Company and the methodology used was analogous to US study by Skinner (1989) who computed the stock prices’ standard deviation using the Black Scholes model and then matched them to actual values and realized values for the stipulated period of three weeks. Options This a contract that presents the buyer with a right but not an obligation to purchase or trade an underlying asset at a given price (strike price) on or prior to a stipulated date (exercise date). An option is a security like a bond or a stock. There are two types of options namely; put and call option; a call option presents the holder with a right to purchase an asset at a given price within an agreed time. Calls translate to holding stock for a long position. Those interested in buying calls anticipates increase in price of stock prior to the maturity of the option. On the other hand, a put option presents the seller with right to trade an asset at a given price with a stipulated period. Similarly, puts compares to holding a stock for a short position. Buyers of puts anticipate the stock price to fall prior the maturity of the option (Barth & Clinch, 1996). Mispricing The option was identified as being mispriced because its put price was relatively lower than the exercise price. For a call option, the value of call should be greater than the value of the underlying asset, which is equal to the strike price if the option is not mispriced. On the other hand, the value of a put should be greater than the strike price and value of the underlying asset. This means that it would have been more advantages to hold the option contract up to the end of the expiration period. On the other hand, options are said to be mispriced if the theoretical prices are less than the option actual prices (Skinner, 1989). However, evidence of mispricing can also be noted if actual prices are higher than theoretical prices. This was the criteria used by the report to ascertain that BHP Company call options were actually mispriced. BHP call option prices were not constant but kept on changing from time to time for the period of three weeks. When the actual prices were higher than the speculative prices, implied volatility was higher as compared to historical volatility as noted by Aitken et al, (1994). Similarly, when theoretical prices were lower than the actual prices, then it was noted that the implied volatility was lower as compared to historical volatility. This formed the bases for identifying that the BHP call options were mispriced as the last three weeks of the option actual market prices were characterized by overvaluing and undervaluing of the option. While implied volatility was greater than historical volatility for BHP call options, prices for the options were below actual prices hence undervalued. Strategies In case the option is mispriced; this would call for a buying strategy, as the buyers will benefit from theoretical discount. On the other when historical volatility for BHP Company were less than implied volatility it was noted that the call options were overpriced. In this case selling strategy was the most appropriate to prevent option holders from losing. However, any option may be based under three strategies that are comprised of the put option, underlying asset as well as the call option. Although, the largest part of arbitrage strategies are based on the notion of synthetics. This may form a part of the best strategies to be adopted by the BHP Company to protect the call option for further mispricing. This strategy involved combination of two parts of the option, either the calls together with the put or the underlying in order generate a position that resembles the third one. For instance, if the buyer opts to purchase the put and the call option, he is likely to make profits in case the prices shoots up, but his loss is mitigated when prices falls (Mayhew & Mihov, 2000). This is equivalent to the same benefit or loss he would suffer in case he chose to purchase the call option. This implies that the buyer of a call option from BHP Company will make money when the market prices goes up but in case the prices in the market fall the loss will be limited to premium. Arbitrage involves synthetics since all fundamental option strategies encompass a synthetic equivalent. In case the benefits and the loss are the same for similar strike prices, therefore a synthetic position need to have similar prices with actual position. The same applies when the strike prices for options are similar as synthetic for call option to be priced the same as the actual call. Arbitrage strategies are comprised of conversions, Jelly Rolls, Reversals as well as Box Spreads. For instance, if we assume a trader purchases call options at the expense of BHP shares, presumably the market maker being on the other side of the equation. The market marker will be short BHP calls, and is at risk of the increase in prices of BHP shares. To counteract the jeopardy, the market maker has to take a long position pertaining to BHP shares. Option Price Y Slope= δ X Stock Price Delta calculates the sensitivity of the option to price variation of an underlying asset computed from the models of option pricing. However, the trader may as well balance the position by choosing another long position for the option in the market. Although, this will not increase BHP shares liquidity, hence the traders are left with an option to hedge in the underlying market opting to execute on the other end of the transaction. Therefore, trading in the underlying may not terminate the original purchase of shares from BHP. This is so because the delta of an option varies with time depending on the value of the underlying and the time taken for the position to be maintained at delta-neutral and the trader should frequently change his exposure to the underlying through sale and purchase of shares. In order to be in a neutral position, the market marker has to use the delta of the position of the option to determine the number of shares he has to buy. Delta-Neutral Strategy CALLS PUTS September/October, 2013 Options Hide Symbol Last Change Vol Bid Ask Open Int. Strike Symbol Last Change Vol Bid Ask Open Int. quote 14.25 4.15 1.00 10.45 12.00 5.00 55.00 quote 0.04 0.02 233.00 0.01 0.05 447.00 quote 7.75 0.20 1.00 5.70 6.75 12.00 60.00 quote 0.16 0.04 12.00 0.10 0.12 330.00 quote 4.85 -2.15 1.00 3.90 4.40 136.00 62.50 quote 0.29 -0.09 1.00 0.26 0.30 4,118 quote 2.12 0.11 28.00 2.27 2.34 213.00 65.00 quote 0.77 -0.17 41.00 0.74 0.79 2,124 66.51 Current price as of 10/04/2013 04:00:35 PM quote 0.84 0.02 13.00 0.91 0.96 1,926 67.50 quote 2.02 -0.16 3.00 1.86 1.93 3,615 quote 0.30 0.05 5.00 0.29 0.33 13,886 70.00 quote 3.66 1.16 4.00 3.70 4.20 271.00 quote 0.06 -0.02 4.00 0.06 0.10 535.00 72.50 quote 5.05 1.65 8.00 5.90 6.70 91.00 quote 0.03 -0.01 122.00 0.02 0.04 206.00 75.00 quote 6.78 1.18 5.00 8.30 9.00 7.00 quote 0.09 0.04 75.00 0.03 0.01 204.00 77.50 quote 0.00 0.00 0.00 10.75 12.10 quote 0.00 0.00 0.00 0.00 0.03 80.00 quote 0.00 0.00 0.00 11.90 15.15 Delta hedging encompassed maintaining a delta neutral portfolio; as such the position should be rebalanced continuously as the share price changed. When the share price increased delta also increased meaning the position had to be re-balanced to ensure neutral delta. At the beginning of the period the share price was $49, where K =50, time = 3 weeks, r=0.05. An option contact made on 100,000 shares, meant that the selling price was $300,000, according to Black-Scholes the value of this option contact was $240,000. For delta hedging to be effective in this specific contract, three assumptions were made; that the option was on 100,000 shares, there was rebalancing after every week and that volatility was held constant. Using delta neutral at the end of the third week the wealth remained relatively constant. The total value of share at the start of the period was; 49*52200 = $ 2,557,800 At the end of the third week 50.250*(40,000 +19600) = $ 2,994,900 This was an increase of ($2994900-2557800) = $437,100 The cash position change was; cumulative costs $2557800- $2966500 =$(408700) Net share value; $437100-$408700 = $28400-$84 = $ 28,316 On September 16 the stock price for BHP Company was $49 and the cost of the option would be $12, for an October 49 call, which showed that the lapse time is the first Friday of October and that the strike price was 49. The total price of the option contact would be $3.15* 100, which would be equal to $1200. The brokerage fee charged for the call option was $42. Total cost was equivalent to $1242. In this case, a stock option contact is the right but not an obligation to buy 100 shares of BHP Company, In this specific example, for the call option to be worth anything it must be more than the strike price of 49. Since call option contract was $12 per share then it would mean that the breakeven price would be $49 plus $12, which would be equal to $61. In the first week, the stock price was $48, which was slightly less than $49 strike price of the same stock at the beginning of the three-week period. At this level and time, the option contract worth nothing. It was also worth noting that a total amount of $1200 had been paid for the option contact and this meant we are down by $1200. In the second week, the stock price dropped further to 47.375, which was still below the price that we acquired the 100 shares. The option contact at this time was still worth nothing and it would not be appropriate to close the contact. During the third week the strike price rose to $50.25. The strike price increase as the price per share improves. The stock is now worth $15.258* 100 = $1525.8. The profit made from this contact was computed as; ($15.25 - $12)*100 = $325. A profit of $325 would have been realized if the position was closed. Since this was the expiry date, it would mean that it would have been appropriate to sell the option and take the profit made. Date September16 September 23 Expiry Date Stock Price $49 47.375 $50.25 Option Price $12 $12 $15.25 Contract Value $1200 worthless 1525 Paper Gain/Loss $0 $0 $325 The price changes for the duration of the existence of the option contact have meant that a profit of $325 has been realized from trading in the option. Intrinsic Value and Time Value The ASX does not specify the element of premium on an option. However, the premium of an option is dependent on expiry time, underlying stock’s volatility price and the exercise price of the option. The premium is often divided into two distinct parts, time value as well as the intrinsic value. Premium= time value + intrinsic value In this case, the price of the option moved from $12 to $15.25. This change in premium occurs due to the aspect of time and intrinsic value. Principally the price of the option is its time value plus intrinsic value. Time value signifies the probability of the option improving in value while intrinsic value was described as the amount in the money. For a call option this is imply that the strike price is equal to the stock price. Therefore, in this case the price of the option would be; Price of option (premium) = time value +intrinsic value $15.25 = $0.25 + $15 Intrinsic Value This is the difference between the current price of the share and the exercise price of the option and the value is greater than zero. Therefore, an option cannot trade at a value, which is less than the intrinsic value. Call options contains intrinsic value given the share price is more than the exercise price. On the hand put option, contain intrinsic value given that the price of the share does not exceed the excise price. The intrinsic value of an option is realized if the shares are sold or bought at a better price than their current price. The extent to which an option is above or below the actual price in the market determines its mispricing. In- the- Money, At-the-Money and Out-of-the-Money These are terms used in reference to options based on the strike price of the option and the share’s current price. At the money (ATM) – the price of the share is equivalent, or near the strike price. Out of the money (OTM) – strike price of call is above the price of the share and below the put’s strike price. In the money (ITM) – the call’s strike price is below the share’s price and above the put’s strike price Time value In The Money At The Money Out of The Money Time Value of an Option Prior to options expiry it usually trade for a value that is higher than its intrinsic value. The time value is represented by the section of the premium that is above or over its intrinsic value. Methodology The methodology entailed a pair wise comparison of options, which were only differentiated by exercise prices. The Black-Scholes model, developed by Black Fisher in 1976 was adopted as the correct and proficient method of pricing calls and options. However, this being the case, market accomplices utilize equivalent standard deviations to price their calls. This suggestion could be assessed by comparing the obscured standard deviations of corresponding pair of calls. Any inconsistencies in obscured standard deviations in corresponding pairs, is evidence that either the mathematical composition of Black-Scholes Formula is erroneous or the market option is incorrect (Aitken et al, 1994). Although Damodaran and Lim (1991) allow variations of the exercise price and maturity time of paired calls, this study only allowed variation of exercise price. This is prompted by the fact that standard deviations of options with different maturity need not to be equal due to two reasons. First, the alternatives of risk free interest rates for different options with different maturity periods have dissimilar risk attributes which could be biased if used in Black Scholes formula. Secondly, different standard deviations should be used for options with different maturity periods due to changing values of standard deviations. Owing to the fact that many Australian companies pay their dividends twice in a year, Expiry periods of such options would incorporate an ex-dividend time meaning amplified likelihood of early exercise and inaptness of typical Black-Scholes model. A control by Mayhew & Mihov (2000) was adopted to limit disharmony between call and stock options. This entailed documenting option data for only a single day for insertion in the sample after fulfilment of certain provisions. Such as actual occurrence of option trade as verified by non –Zero recordings in the “volume –traded column’ or in ‘daily high/low column and that the ‘last sale’ option price was contained in time period of closing bid/ask for the option. Time to maturity will be calculated using information supplied by clearing house. The likelihood of early exercise through ex-dividend date within maturity period would be reduced by using options, which are within three weeks to maturity. In addition to the cross-section data analysis of observations, the report also incorporated time series analysis to mispricing differences. This was used to establish whether there was any bias in pricing. To achieve this average percentage mispricing error (ME) of BHP Company, mispricing error was calculated as follows (Weate, 1991); ME% = [(Pm-Pt)/ Pm], where: ME is the mispricing error, Pm is the of the option’s market price with the least exercise price in a pair of matched options, Pt is the hypothetical price of the least exercise price option in a matched pair using ISD calculated from data on the superior exercise price option in a matched pair. In this calculation it is hypothesized that the superior exercise price is appropriately prized ,the standard value of ‘ Relative Mispricing error’ (RME) of the least price option is the discrepancy of high price implied standard deviations from low option price implied standard deviations divided by lower exercise price hypothetical standard deviation. Recommendations Things would have been improved by combining two or three options of the same nature on the same underlying asset. Since it would not have been possible to combine two options with different expiry period, it would have been more profitable to combine options with different exercise prices. In this case if there were two calls we would have maintained the call with a lower strike price when the conditions were not favourable. Such a call option should never sell for a lower amount than one with a higher strike price. On the same vein, a put with lower strike price should at no time sell for a more amount than one with a higher strike price, Maintaining this balance would have created a space to observe the movement of the stock price and option value and sell when the condition would have been favourable and thus making more profit. This spread takes advantages of the mispricing of the options on identical underlying asset. In this specific case the contract would have only been closed at least when it is worth something at the end of the third week period. During the second week, the stock price significantly reduced and this pulled down the value of the option. The option contract at this time would have been worth nothing and therefore it was only appropriate to rebalance the position and wait for the expiry date. During the third week the stock price increased and so did the value of the option. At this time closing out position when the value of the option contract was still high was the appropriate move. Due to the lower prices of stock at week two the value of the option was lower than at the beginning of the period meaning it was worth nothing. Improvement in stock prices and rebalancing position using a spread would have increased the returns realized after exercising the option. Work Cited Aitken, Frino, and Jarnecic., ‘Option listings and the behaviour of underlying securities: Australian evidence’, Securities Industry Research Centre: Asia-Pacific paper, 1994. Barth, M., and Clinch G., Scale Effects in Capital Markets-Based Accounting Research, Working paper (Australian Graduate School of Management and Stanford University), 1996 Skinner, D., ‘Options markets and stock return volatility’, Journal of Financial Economics, 1989; 23, 61-78 Damodaran, A. and Lim J., ‘The effects of option listing on the underlying stocks’ return processes’, Journal of Banking and Finance, 1991; 15, 647-664 Mayhew, S. and Mihov V., ‘Another look at option listing effects’. Research paper, University of Georgia, 2000. Print Weate, P., 'Raising Equity Capital, in Bruce, R., B. McKern, I. Pollard, and M. Skully, eds., Handbook of Australian Corporate Finance, 4th edn. (Butterworths, Sydney), 1991. Print Read More