Collection and Summary of the Options Market Information for Apple - Case Study Example

DERIVATIVE SECURITIES By (Name) Institution Instructor Class/Course City Collection and Summary of the Option Market Information for Selected Underlying Firms The spreadsheet below shows the Top Ten most active options information in the ten underlying firms. MOST ACTIVE OPTIONS: Last updated: Thu, Jul 31, 2014, 10:50AM EDT Ticker Option Symbol Option Close Close Change ($) Close Change (Rate) Volume Volume Change Volume Change (Rate) Open Interest Open Interest Change Open Interest Change (Rate) Intrinsic Value of Option ($) MWE MWE150117C00035000 JAN 15 35 Call 34.8 -0.10 (-0.30%) 313,280 313,280 0.00% 9,775 -449 (-4.40%)  0.10 (out of the money ) SPY SPY140816P00194000 AUG 14 194 Put 2.64 1.71 (+183.90%) 98,947 77,519 (+361.80%) 168,784 3,025 (+1.80%)  1.71(in the money) XLE XLE140920P00098000 SEP 14 98 Put 3.38 1.34 (+65.80%) 78,401 78,302 (+79092.90%) 81,366 37 0.00%  1.34 (in the money) XLF XLF141220C00027000 DEC 14 27 Call 0.02 -0.01 (-40.00%) 53,628 53,628 0.00% 86,125 0 0.00% 0.01(out of the money) IWM IWM140816P00110000 AUG 14 110 Put 1.38 0.87 (+171.60%) 51,267 38,173 (+291.50%) 102,965 -3,343 (-3.10%) 0.87(in the money) EEM EEM150117P00041000 JAN 15 41 Put 1.36 0.28 (+25.90%) 51,127 51,116 (+464690.90%) 52,781 1 0.00% 0.28 (in the money) FXI FXI140920P00035500 SEP 14 35.5 Put 0.13 0.02 (+19.00%) 51,035 51,035 0.00% 61,008 0 0.00% 0.02(in the money ) EWT EWT140816P00016000 AUG 14 16 Put 0.34 0.24 (+252.60%) 38,058 38,048 (+380480.00%) 65,844 0 0.00% 0.24 (in the money) QQQ QQQ140816P00094000 AUG 14 94 Put 0.76 0.51 (+198.00%) 33,834 33,209 (+5313.40%) 63,802 -47 (-0.10%) 0.51 (in the money) F F141220C00018000 DEC 14 18 Call 0.46 -0.13 (-21.60%) 32,024 31,831 (+16492.70%) 13,016 154 (+1.20%) 0.13(out of the money) Source: fiance.yahoo.com According to Hull & Suo (2002), the intrinsic value is the difference that exists between the underlying’s price and the strike price. More specifically, a call option has an intrinsic value that is equal to the underlying price less the strike price whereas a put option has an intrinsic value of the strike price less the underlying price. Wang (2013) states that as the strike price has a lesser value than the current underlying price, then the call option is referred to as the in-the money. A put option is called the in-the money if its strike price is greater than the current underlying price. The last digit of the sum of the IDs ends with 2. Firm ‘SPY’ is ranked number 2. Expiration Date Symbol Strike Price best Bid Best Offer Volume Open Interest Implied Volatility 20130823 101404504 (call) 310000 145.85 147 0 0 20130823 101404521 310000 0 0.13 0 0 0.597246 20130921 100964276 210000 245.9 247 4 2 0 20131019 101235375 210000 245.85 247 0 0 0 20131019 101235376(put) 210000 0 0.12 0 0 0.591799 20130921 100964276(call) 210000 245.9 247 4 2 0 20130921 100964367(put) 210000 0 0.04 0 3 0 20131019 101235375(call) 210000 245.85 247 0 1 0 20131019 101235376(put) 210000 0 0.12 0 0 0.591799 20131116 101294972(call) 215000 240.85 242 0 0 0 20140118 83181928(call) 1000000 0.05 0.14 0 18357 0.401991 20140419 101230987(call) 200000 255.6 257.15 0 1 0 20150117 83244103 1000000 1.45 1.65 4 5687 0.319665 In examining the effects of the strike price and the maturity on the option prices, it is important to note that options are financial instruments that extend to investors the right to purchase or sell a stock at an agreed-upon price on or before a specific date. In this case, therefore, the option's time horizon plays a key role in determining its price. Clearly, as shown in the above table, expiration time has a great influence on the option maturity and therefore price. For instance, as argued by Kumar, et al. (p713-6), a call option is the right but not the obligation to purchase a stock at a specific price on or before a certain time. Basically, the price at which the call option buyer can purchase the underlying stock is called the strike price, while the date when the option expires is called the expiration date. As the expiration date draws near, so does the maturity of the option. Ideally, the longer the tenor of an option, the higher the price of the option, in the event that the underlying price of the stock remains constant. Ni, et al. (p 1052-3), states that time value is a the amount an investor is willing to pay for an option above its intrinsic value, in the hope that at some time prior to expiration its value will increase. Although time value will decrease as the expiration date of an option draws near, the value of a call option can increase if the underlying price of the stock increases (Rhoads, 2014). The tables below shows a call/put option pattern that help illustrate the differences between the covered call and the protective put. In order to earn a profit in a stock market, it is important to use well determined combinations of strategies that will both enable you to make a profit, yet at reduced risks. In this case, since the prices of options depend on the prices of their underlying securities, options can be used in various combinations to earn profits with reduced risk, even in directionless markets. Some of the simplest option strategies are the covered call and the protective put. As stated by Rhoads (2014), the protective put option strategy is used when an option trader (investor) still intends to hold his stock but is uncertain of the risks that may be involved in the near future. It is therefore more of a hedging strategy than risk taking strategy, whereby, the investor buys a put to guard against the drop in the stock price of the stock option. It is thus, used as a means to protect unrealized gains on shares from a previous purchase. On the other hand, a covered call is a strategy in which the investor holds the underlying and sells a call option against a long stock as a means of hedging risk and smooth volatility (Rhoads, 2014). This strategy basically involves writing a call for stock already owned. One of the striking differences between these two options (the covered call and the protective put) is that the covered call does not regard how high the stock rises as the covered call writer’s maximum payoff will be the strike price and the premium received for the call. However, as the stock price decreases below the strike price of the protective put, the put increases in value and thus keep the payoff at the same level. In this case for the put, therefore, the net payoff of the put after deducting the premium paid for the put is below the strike price as shown in the graph above. Consider the differences in the table below; Covered call Protective put The initial value = the initial value of the underlying – the call premium  The initial value = the initial value of the underlying + the put premium  The value at any time = the value of the underlying plus the value of the short call  The value at any time = the value of the underlying plus the value of the long put The maximum profit occurs when the option is exercised: maximum profit will be: exercise price – initial stock price + call premium This strategy has no maximum profit because if the put option expires worthless (i.e. when prices keep increasing), the upside profit is unlimited (infinity). Historical Volatility for APPLE INC a. Prices of different financial assets like currencies and stocks are regularly changing as the traders buy and sell them. This variation of the prices over a specified period of time is the volatility based on the financial historical data. Apple Inc. (AAPL) historical data Historical Prices Top of Form Set Date Range Start Date: day Year Eg. Jan 1, 2010 End Date: day Year Daily Weekly Monthly Dividends Only Bottom of Form Prices Date Open High Low Close Volume Adj Close* Jul 31, 2014 97.16 97.45 95.33 95.60 56,843,000 95.13 Jul 30, 2014 98.44 98.70 97.67 98.15 33,010,000 97.66 Jul 29, 2014 99.33 99.44 98.25 98.38 43,143,000 97.89 Jul 28, 2014 97.82 99.24 97.55 99.02 55,318,000 98.53 Jul 25, 2014 96.85 97.84 96.64 97.67 43,469,000 97.19 Jul 24, 2014 97.04 97.32 96.42 97.03 45,729,000 96.55 Jul 23, 2014 95.42 97.88 95.17 97.19 92,918,000 96.71 Jul 22, 2014 94.68 94.89 94.12 94.72 55,197,000 94.25 Jul 21, 2014 94.99 95.00 93.72 93.94 39,079,000 93.48 Jul 18, 2014 93.62 94.74 93.02 94.43 49,988,000 93.96 The calculation in the spreadsheet below gives the column of the % Change that is calculated using each day’s closing price and represents the return series that is the % change in price from one day to another. After the %change column, the standard deviation is calculated from the daily returns, which has been calculated using excel. In excel the Standard Deviation is calculated using the =StdDev. This formula takes the range of data as its input such as the % change data. The standard deviation has been calculated for the 10 days period as shown below. Date Open High Low Close Volume Adj Close* change % std 31-Jul-14 97.16 97.45 95.33 95.6 56,843,000 95.13 -2.66 -2.66 30-Jul-14 98.44 98.7 97.67 98.15 33,010,000 97.66 -0.24 -0.24 29-Jul-14 99.33 99.44 98.25 98.38 43,143,000 97.89 -0.65 -0.65 28-Jul-14 97.82 99.24 97.55 99.02 55,318,000 98.53 1.36 1.36 25-Jul-14 96.85 97.84 96.64 97.67 43,469,000 97.19 0.66 0.66 24-Jul-14 97.04 97.32 96.42 97.03 45,729,000 96.55 -0.17 -0.17 23-Jul-14 95.42 97.88 95.17 97.19 92,918,000 96.71 2.54 2.54 22-Jul-14 94.68 94.89 94.12 94.72 55,197,000 94.25 0.82 0.82 21-Jul-14 94.99 95 93.72 93.94 39,079,000 93.48 -0.55 -0.55 18-Jul-14 93.62 94.74 93.02 94.43 49,988,000 93.96 1.42 1.42 1.440394 The standard deviation is 1.44%. This figure represents the volatility of the ten day period calculated above of APPLE Inc. b. Using past 50 days' returns to estimate daily volatility and check how the AAPL volatility has changed over time, the standard deviation for the 10 daily data is 1.44%. This has been used to represent a 1-day volatility. This data can also be used to get the 50 day volatility data using the annualized volatility as below. (1-day volatility)(Sqrt of 50) (1.44)(Sqrt 50) 1.44*7.07 10.18% Maximum volatility=2.53% Minimum volatility=1.41% Average volatility=1.53% A stock whose price varies wildly (meaning a wide variation in returns) will have a large volatility compared to a stock whose returns have a small variation. The variation in the prices over a period of time is the volatility. The volatility shows how turbulent the price is and is an indicator of the risk involved. As illustrated by the graph above, and also as argued by Watkins (2014), there is a strong relationship between volatility and stock market performance. Volatility tends to decline as the stock market rises and increase as the stock market falls. When volatility increases, risk increases and returns decrease. Basically, the greater the dispersion of returns around the mean, the higher the decline in the return and the reverse is also true. The volatility does seem constant at some point because the strike price also seem stable, thereby strongly embracing the fact that stable stock prices implies stable volatilities as shown in the graph above. AAPL Puts Using Spreadsheet "Puts and Dvd.Xlsx" 1) In calculating the AAPL stock prices using the spreadsheet of the ‘puts and Dvd. Xlsx’, a binomial probability distribution is used. In support of the binomial model, a binomial tree is used representing an increasing stock price as time increases (horizontally). In this case, a statistical or mathematical comparison between the price provided by "Puts and Dvd xlsx" with the price given at "Option Price’’ shows a great contrast between them. They are not the same because in the prices given at the "Option Price’’ data increases with maturity date while the prices provided by "Puts and Dvd xlsx" increases as time increases(horizontally) and is thus calculated binomially. The binomial nature of the prices provided by the data "Puts and Dvd xlsx" best explains the differences that exist in the prices of two information sets. 2). In the event that all the input variables are kept constant except the rate, the following effects will be notified in the whole pricing system of the options. Consider the table below, Before the changes are made, the input variables are Input Variables: rate q Stock Price =S Strike Price =X Sigma () Settlemet date (i.e., today) Option Expiry Date Next Dvd Pmt Date Dividend Pmt 0.1250% 0.34% 456.68 450 0.2232 8/1/2013 9/21/2013 8/8/2013 1.74284 Binomial tree: u d a P Smax Smin 1.011869 0.98827 0.999993992 0.496795667 823.8071958 253.1619334 Black's Model: Euro. Put Euro. Put Amer. Early exercise d1 d2 N(-d1) N(-d2) (Black-Scholes) (Bin. Tree) put premium 0.168902 0.08547 0.432936797 0.46594382 12.77259 12.84591 12.77259 0.00000 Dividend payments: Next Dvd (days) Days Betw. Dvds First coupon pmt priod # of periods between pmts PV(Dvds) 7 91.25 7 89 1.742797385   Dividend pmt: 0 0 0 0 0 0 0 Discount factor: 1 0.999996507 0.999993014 0.999989521 0.999986027 0.999982534 0.99997904 PV(Dividends): 1.742797385 1.742803472 1.74280956 1.742815648 1.742821736 1.742827824 1.74283391   0 1 2 3 4 5 6 Stock 0 456.68 462.0796355 467.5433589 473.0719309 478.6661213 484.3267088 490.05448 Amer. 0 12.84591039 10.5081129 8.44634741 6.660089165 5.142444547 3.880325568 2.85504326 1 451.3437129 456.6800122 462.0796476 467.5433711 473.0719431 478.66613 1 15.15402355 12.54369328 10.20991502 8.158451731 6.388525241 4.89257711 2 . 446.0700192 451.3437251 456.6800244 462.0796598 467.54338 2 . 17.7312146 14.84783628 12.23532234 9.905893583 7.86546575 3 . . 440.8581845 446.0700313 451.3437373 456.68004 3 . . 20.57799413 17.42718108 14.5351691 11.9204039 4 . . . 435.7074834 440.8581967 446.07004 4 . . . 23.68882218 20.2824822 17.1167343 5 . . . . 430.6171987 435.7075 5 . . . . 27.05194444 23.4080528 When the input variable varies with time, there is an increasing stock price and a decreasing effect on the price of American Sep 2013 Put 450 AAPL on August 1, 2013. However, when the input variables are kept constant except the rate left at its normal movement as shown below, the reverse effects take place as the price of American Sep 2013 Put 450 AAPL on August 1, 2013 increase across time. Option pricing (puts) 3). Keeping all inputs constant except for "Sigma ()" to show how volatility would impact the price of American Sep 2013 Put 450 AAPL on August 1, 2013 When the sigma is kept varying while other input variables are kept constant, an effective changes are instantly shown, consider the table and graph above. Before other variables like rate, q, stock price as well as the strike rice is made constant; the stock prices were increasing horizontally, i.e. increasing as time increases. However, when all these variables are made constant except sigma, the opposite effects take place. First, it is noticeable that the stock prices decreases as time increases in a horizontal spectrum. Secondly, putting all variables constant except sigma make the price of American Sep 2013 Put 450 AAPL to have an increasing effect on August 1, 2013. As argued earlier, volatility is the variation of the prices over a specified period of time. Thus, the volatility of the American Sep 2013 Put 450 AAPL increases with time when other input variables are kept constant as the sigma is kept varying with time as shown the graph and table below. Input Variables: rate Q Stock Price =S Strike Price =X Sigma () Settlemet date (i.e., today) Option Expiry Date Next Dvd Pmt Date Dividend Pmt 1.0000% 1.00% 1 1 0.2232 8/1/2013 9/21/2013 8/8/2013 1.74284 4 Binomial tree: u D a p Smax Smin 1.011869 0.98827 1 0.497050266 1.803904694 0.554353012 Black's Model: Euro. Put Euro. Put Amer. Early exercise d1 d2 N(-d1) N(-d2) (Black-Scholes) (Bin. Tree) put premium   #NUM! #NUM! #NUM! #NUM! #NUM! 1.74007 #NUM! 0.00209   Dividend payments: Next Dvd (days) Days Betw. Dvds First coupon pmt priod # of periods between pmts PV(Dvds) 7 91.25 7 89 1.742499105   Dividend pmt: 0 0 0 0 0 0 0 1.74284 Discount factor: 1 0.999972055 0.999944111 0.999916168 0.999888225 0.999860284 0.99983234 0.999804 PV(Dividends): 1.742499105 1.7425478 1.742596497 1.742645195 1.742693894 1.742742595 1.7427913 0   0 1 2 3 4 5 6 7 Stock 0 1 0.991236006 0.982367417 0.97339299 0.964311469 0.955121583 0.945822 -0.8064 Amer. 0 1.742158277 1.751018174 1.759983148 1.769054448 1.77823334 1.787521104 1.79691903 1.806428 1 1.008758013 1.000097392 0.991333401 0.982464814 0.973490389 0.9644089 -0.7876 1 1.733499105 1.74225565 1.751116042 1.760081516 1.769153324 1.77833273 1.787621 2 . 1.01741387 1.008855408 1.000194789 0.991430801 0.9825622 -0.7693 2 . 1.724941591 1.733595993 1.742353028 1.751213915 1.76017989 1.769252 3 . . 1.025968769 1.017511267 1.008952808 1.0002922 -0.7513 3 . . 1.716484545 1.725038001 1.733692887 1.74245041 1.751312 4) Understanding the option pricing strategies is one of the critical tools of an investor in an option security market. The factors that determines the value of the options in the market must be well analyzed, factors like the intrinsic value, time to expiration (the time value), volatility, cash dividends, and more importantly the interest rates. For a put option the intrinsic value is the strike price minus the underlying price. In this case, for the intrinsic values that are in-the-money, the strike price must be greater than the underlying price. In the analysis of the "April 2015 AAPL 100 Put" option, consider the given input variables, going with the same rates of variations, then the values of the pricing option "April 2015 AAPL 100 Call" would change using the same binomial tree used in the above cases as shown in the table below; Option Pricing (Puts) 4/1/2015 Input Variables: rate q Stock Price =S Strike Price =X Sigma () Settlemet date (i.e., today) Option Expiry Date Next Dvd Pmt Date Dividend Pmt 0.1250% 0.34% 456.68 450 0.2232 4/1/2015 9/21/2013 8/8/2013 1.74284 Binomial tree: u d a p Smax Smin 1.10497 0.905002 0.999570092 0.472916297 67163.59594 3.10520334 Black's Model: Euro. Put Euro. Put Amer. Early exercise d1 d2 N(-d1) N(-d2) (Black-Scholes) (Bin. Tree) put premium 0.038781 -0.66704 0.484532317 0.747626365 159.74216 157.99255 159.74956 0.00739 Dividend payments: Next Dvd (days) Days Betw. Dvds First coupon pmt priod # of periods between pmts PV(Dvds) -601 91.25 -8 1 88.33164025   Dividend pmt: 1.74284 1.74284 1.74284 1.74284 1.74284 1.74284 1.74284 Discount factor: 1 0.999750031 0.999500125 0.999250281 0.9990005 0.998750781 0.99850112 PV(Dividends): 86.58880025 84.86761015 83.14598971 81.4239388 79.70145733 77.97854519 76.2552023   0 1 2 3 4 5 6 Stock 0 454.93716 491.8814521 532.8840249 578.3709205 628.8129029 684.7301519 746.69745 Amer. 0 157.9999435 139.8685772 122.0813485 104.9039565 88.59948657 73.41396659 59.5612608 1 418.2236294 451.4943495 488.4377808 529.4394925 574.9255269 625.36665 1 174.3429332 155.8941947 137.5513634 119.5826096 102.2664478 85.8778809 The main effects on the on August 18, 2014 options are due to the changing rates of interest as time increases. 5) Using the information above, the information and "Puts and Dvd xlsx" the price Option of April 2015 AAPL 100 Call on August 18, 2014 would be as shown in the table below; rate q Stock Price =S Strike Price =X Sigma () Settlemet date (i.e., today) Option Expiry Date 0.1250% 0.34% 456.68 450 0.2232 8/18/2014 4/1/2015   Binomial tree: u d a p Smax Smin 1.10497 0.905002046 0.99957 0.472916 67163.6 3.1052033 Black's Model: Euro. Put Euro. Put Amer. d1 d2 N(-d1) N(-d2) (Black-Scholes) (Bin. Tree) put 0.038781 -0.667038924 0.484532 0.747626 159.74216 0.00000 159.74956 Dividend payments: Next Dvd (days) Days Betw. Dvds First coupon pmt priod # of periods between pmts PV(Dvds) Payoff European -601 #DIV/0! -8 #DIV/0! 88.33164   1.74284 put 0.987578   Stock 0 454.937 491.881 532.884 578.371 628.8129 684.73 1.74284 0 Amer. 0 157.9999 139.8686 122.0813 104.90396 88.599487 73.41397 54174.5   1 418.224 451.494 488.438 529.4395 574.926 0 0 1 174.3429 155.8942 137.55136 119.58261 102.2664 44370.8   2 . 384.834 414.78 448.0498 484.992 0 0 2 . 190.9784 172.42592 153.73875 135.1759 36341.2   3 . . 354.452 381.3893 411.335 0 0 3 . . 207.71493 189.27443 170.4668 29764.8   4 . . . 326.7925 351.007 0 0 4 . . . 224.35887 206.239 24378.6   5 . . . . 301.596 0 0 5 . . . . 240.723 19967.1   References Blasco, N, Corredor, P, & Santamaría, R 2010, 'Does informed trading occur in the options market? 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Kumar, R, Sarin, A, & Shastri, K 1998, 'The Impact of Options Trading on the Market Quality of the Underlying Security: An Empirical Analysis', Journal Of Finance, 53, 2, pp. 717-732. Ni, S, Pan, J, & Poteshman, A 2008, 'Volatility Information Trading in the Option Market', Journal Of Finance, 63, 3, pp. 1059-1091. Rhoads, R 2014, Trading Weekly Options : Pricing Characteristics And Short-Term Trading Strategies, Hoboken, New Jersey: Wiley. Wang, Y 2013, 'Volatility Information in the Trading Activity of Stocks, Options, and Volatility Options', Journal Of Futures Markets, 33, 8, pp. 752-773. Watkins, J 2014, 'US options trading surge in first quarter', Foi: Future & Options Intelligence, 1913, p. 16. Read More