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29.04.2015 admin
The large number of strike prices covered by options on Eurodollar futures makes them an excellent source of data to use in building analytical pricing models. LLP price curves permit forecasting option prices based on the relationship between underlying asset prices and strike prices. Eurodollar options, like other exchange-traded options, are valued continuously by computer trading systems based on theoretical models such as Black-Scholes. Eurodollar futures prices are equal to 100 less the 90-day interest rate for a given forward month. When the futures price equals the strike price there is no intrinsic value and the option price reflects only time premium. The pricing of call options, like everything on Wall Street, is based on supply and demand created by the buyers and sellers of that option at that point in time. Clearly the difference between the strike price and the current price is the most important factor.
Once you understand those 3 elements, then learn to start thinking of option prices as having 2 components.
Understanding Pricing of Call Options: Let me explain the pricing of call options by walking you through the 3 bullet points above. Take a look at the chart below which shows AAPL options for January and you will see that the call options with the lower strike prices are more expensive than the higher strike prices. The second important factor that influences the price is the number of days left until the call or put expires.
The third important factor that influences the price is the expected volatility of the stock in the days remaining to expiration. Call and Put Trading Tip: Actually, we are more concerned with trading days left than calendar days.
Logically, the February $310 call will be more expensive than the January $310 call, and the March $310 call will be more expensive than the February.
Books about option trading have always presented the popular strategy known as the covered-call write as standard fare. At the time these prices were taken, RMBS was one of the best available stocks to write calls against, based on a screen for covered calls done after the close of trading. Figure 1 - RMBS May option prices with the May 25 in-the-money call option and downside protection highlighted. Alternative Covered Call Construction As you can see in Figure 1, we could move into the money for options to sell, if we can find time premium on the deep in-the-money options. Looking at another example, a May 30 in-the-money call would yield a higher potential profit than the May 25. While there is less potential profit with this approach compared to the example of a traditional out-of-the-money call write given above, an in-the-money call write does offer a near delta neutral, pure time premium collection approach due to the high delta value on the in-the-money call option (very close to 100).


The Bottom LineCovered-call writing has become a very popular strategy among option traders, but an alternative construction of this premium collection strategy exists in the form of an in-the-money covered write, which is possible when you find stocks with high implied volatility in their option prices. To create a synthetic short position of 100 UVXY shares, I would sell one call option and buy one put option, both with a strike price of 42.00. Granted, brokerage costs are higher than if my broker can find the shares to borrow…but when that is not an option, I would rather pay higher brokerage fees and be short UVXY than miss the trade entirely. In contrast, the LLP system assumes all of the variables necessary to calculate theoretical option values are included in market prices.
Beyond this simple supply and demand explanation of option pricing, you should also know that there are several formulas that Wall Street mathematicians have developed to approximate a fair price of call and put options. These are the "in-the-money" value (also called the intrinsic value) and the time value (also called the risk premium). First is the difference between the the strike price of the option and the underlying stock. If today is January 1st and we are comparing the prices of the AAPL January $310 call to the February $310 call, then the January option has about 15 calendar days left and the February option has about 45 days left until expiration. Naturally, the prices of options on very volatile stocks are more expensive than the price of low volatility stocks. Since the option markets are closed on the weekend and Holidays, the January options might have only 11 trading days left and the February options might have only 33 trading days left. We can begin by looking at the prices of May call options for RMBS, which were taken after the close of trading on April 21, 2006.
As you can see in Figure 1, it would be possible to sell a May 55 call for $2.45 ($245) against 100 shares of stock. This is because the cost basis is much lower due to the collection of $1,480 in option premium with the sale of the May 25 in-the-money call option.Potential Return on in-the-Money Call Writes As you can see in Figure 2, with the May 25 in-the-money call write, the potential return on this strategy is +5% (maximum). I have found that upon options settlement, if UVXY is still hard-to-borrow (it generally is), a couple days can pass while the broker tries to find the shares. This curve is computed by a system that depends on a log-log parabolic regression equation, the LLP option-pricing model. The resulting price curves reflect that both the LLP and theoretical models use logarithms in their calculations and that LLP parabolic price curves are closely related to those generated by theoretical models. Likewise the right to by GOOG in 3 months at $650 should be worth more than the right to buy GOOG at the same price in 30 days. A call option to buy AAPL at $335 when AAPL is trading at $340 is "in-the-money" $5 so you know the price will be at least $5. I hope it is clear that if the AAPL stock is at $300 then the $310 call would be more expensive than the $320 call; and the $320 call would be more expensive than the $330 call, etc. Stocks that move frequently move a couple of dollars a day (like Google) generally have expensive options compared to a stocks that only move a dime or two a day (like General Electric).


It involves writing (selling) in-the-money covered calls, and it offers traders two major advantages: much greater downside protection and a much larger potential profit range.
RMBS closed that day at 38.60, and there were 27 days left in the May options cycle (calendar days to expiration). This traditional write has upside profit potential up to the strike price, plus the premium collected by selling the option. Downside protection from the sold call offers only 6% of cushion, after which the stock position can experience un-hedged losses from further declines. These conditions appear occasionally in the option markets, and finding them systematically requires screening. Predictive formulas for option prices would have enabled traders to forecast movements in September 2007 calls based on changes in the futures price throughout several days or weeks following each date. Although the LLP method is useful for analyzing any options, the emphasis here is on its value in creating Eurodollar price curves. To the final point of volatility, since GOOG can easily fluctuate $10 in a day, the GOOG options should be priced more than the GE options whose stock price fluctuates 50 cents or less in a day.
On the topic of volatility, it is also important to note that the prices of options frequently get more expensive during the week of an expected earnings announcement and then return to normal the day after an earnings release.
Option premiums were higher than normal due to uncertainty surrounding legal issues and a recent earnings announcement. At that point, I let them do that…then open a new synthetic short position using new options.
That extra $1 is called the time value or risk premium and it represents the extra amount the market is willing to pay to basically bet the price of AAPL will continue to go up.
If we were going to do a traditional covered-call write on RMBS, we would buy 100 shares of the stock and pay $3,860, and then sell an at-the-money or out-of-the-money call option. The short call is covered by the long stock (100 shares is the required number of shares when one call is exercised). If we were to annualize this strategy and do in-the-money call writes regularly on stocks screened from the total population of potential covered-call writes, the potential return comes in at +69%. If you can live with less downside risk and you sold the May 30 call instead, the potential return rises to +9.5% (or +131% annualized) - or higher if executed with a margined account.



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