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FIGURE 4.4 Values of carry ( SRT) and total return of carry as time approaches zero. cash market does not close until 5 P.M. EST, so there is a two-hour window of opportunity when an investor holding a short future may profit from a decline in the cash market. In actuality, the market often does not really close at 5 P.M., remaining open for as long as there is a trader willing to make a market. Indeed, even if one is hard pressed to find a market maker in the United States after 5 P.M., it may not be difficult to find a market maker in Tokyo where the trading day is just getting under way. The wildcard option thus values the opportunity to profit from different trading hours for cash and futures. Finally, the timing or cost-of-carry option attempts to quantify the optimal time to make delivery. If there is a positive cost-of-carry, then there is an incentive to put off delivery until the last possible delivery date. Cost-of-carry means the difference between the return earned on a cash security and the cost to finance that cash security in the repo market. If that difference is positive, then there is a positive cost-of-carry. Cost-of-carry is usually positive when the yield curve has a normal or positive shape. Conversely, if there is a negative cost-of-carry, then there is an incentive to make delivery on the first possible delivery date. Negative cost-of-carry exists if there is a negative difference between the return earned on a cash security and the cost to finance that cash

The more volatile the underlying security, the more expensive it will become to manage the synthetic option This is consistent with the fact that an increase in volatility serves to increase the value of a true option The term implied delta means the value delta would be for a traditional option when valued using the objective strike price and expected volatility Just how we draw a synthetic option s profit/loss profile depends on a variety of assumptions For example, since the synthetic option is created with Treasury bills and forwards, are the Treasury bills financed in the repo market If yes, this would serve to lever the synthetic strategy It is an explicit assumption of traditional option pricing theory that the risk-free asset (the Treasury bill) is leveraged (ie, the Treasury bill is financed in the repo market).

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reg clsid = "{08632905-0B63-45B5-B388-30C73CAE611C}" public methods = \ [ "CreateHullWhiteLatticePricer" , "InvokePricer" ] pricers = {} retrieve = staticmethod( lambda tag, which : utils.retrieve( pricer server , PricerServer , tag, which)) def CreateHullWhiteLatticePricer( self , tag , trade id , env id , num states , num std dev): try: from trade server import TradeServer from market server import MarketServer trade = TradeServer.retrieve(trade id, trades ) env = MarketServer.retrieve(env id, environments ) model args = {"num states": num states, "num std dev": num std dev} factory = ppf.model.hull white lattice model factory() model = factory(trade, env, model args) pricer = ppf.pricer.lattice pricer(trade, model, env, None) PricerServer. pricers[tag] = pricer return tag except RuntimeError, e: ppf.com.utils.raise com exception(e) def InvokePricer(self, tag): try: return PricerServer.retrieve(tag, pricers ). call () except RuntimeError, e: utils.raise com exception(e) if name == " main ": utils.register com class(PricerServer)

1 Any standard option-pricing model can be modified to allow for the pricing of options where the underlying price series is not normally distributed 2 When an implied volatility value is calculated, it may well embody more value than what would be expected for an underlying price series that is normally distributed; it may embody some kurtosis value Perhaps for obvious reasons, historical volatility often is referred to as a backward-looking picture of market variation, while implied volatility is thought of as a forward-looking measure of market variation Which one is right Well, let us say that it is Monday morning and that on Friday a very important piece of news about the economy is scheduled to be released maybe for the United States it is the monthly employment report with the potential to move the market in a big way one direction or the other.

Let us assume an investor was looking to buy a call option on the Dow Jones Industrial Average for expiration on Friday afternoon To get a good idea of fair value for volatility, would the investor prefer to use a historical calculation going back 20 days (historical volatility) or an indication of what the market is pricing in today (implied volatility) as it looks ahead to Friday s event A third possibility would involve looking at a series of historical volatilities taken from the same key week of previous months to identify any meaningful pattern It is consistently this author s preference to rely upon implied volatility values.

Repo financing on a synthetic option that is structured with a string of overnight repos is consistent with creating a synthetic American option, which may be exercised at any time Conversely, the repo financing structured with a term repo is consistent with a European option, which may be exercised only at option maturity Since there is no secondary market for repo transactions, and since investors may not have the interest or ability to execute an offsetting repo trade, a string of overnight repos may be the best strategy with synthetic options By going long a forward, we are entering into an agreement to purchase the underlying security at the forward price Thus, if the actual market price lies anywhere above (below) the forward price at the expiration of the forward, then there is a profit (loss).

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