In-the-money

Money Flows. Estimation of sales revenues and manufacturing expenses has been discussed. Depreciation, part of the manufacturing expense, is treated separately in the money flow, as is interest. 

The night was young yet, but I was happy not to have to talk any more. I fetched the scales and a heavy bag from the secret cache. While the Maestro watched in sullen silence, I counted out one hundred sixty-three sequins and weighed them. I added two ducats and two lira and put the lot in the money pouch. It weighed more than a pound, but it was not bulky. 

Allow savings to build up in the money market account until you have a balance at least equal to three months , and preferably equal to six months , net take home pay. This is your emergency fund. Save it to cover times when your income is interrupted by illness, disability, or unemployment. When your emergency fund is in place, consider investment alternatives for your savings. 

By traditional methods, a project is considered successful if it is built on time, is in the money, and technically works. This method of analyzing project success is one of the reasons returns on projects are so low. With this method, we have not measured how well we have achieved the scope. 

Compatibility with older programs is important because people have a significant investment in the money spent on their programs and in their time learning how to use them. Microsoft built a number of features into Windows 9x that allow previous users of DOS and Windows 3.x to capitalize on their investment and that allow technicians access to DOS-based troubleshooting. 

For risk-free investments, such as U.S. Treasury bills, the required return (as a percent of the capital invested) is determined by supply and demand in the money markets. If the going risk-free interest rate is 5 percent per year, for example, an investor who puts up 100 expects to get at least 105 back next year. From another point of view, 100 promised for delivery next year is worth only 95.23 today, because the investor could take that 95.23, invest it in a risk-free security, and have the 100 a year hence. Not having access to the 95.23 today essentially deprives the investor of the opportunity to invest at the going interest rate. 

Overall, the lEE performs accurately for in-the-money and at-the-money options (see figure (4.3)). The relative and absolute deviation from the cdf is only about Arei K) th Aabs K) w 10 — 10 . We obtain less accurate figures only for far-out-of-the money options with an absolute approximation error of about Aabs K) w 10" - 10" , together with a relative error of A,/(/T) 10-4-10"2. 

Furthermore, we find that the impact of this de-correlation increases with an increase in the moneyness... 

First, the option price increases with the correlation for in-the-money and at-the-money options (moneyness < 1-075). By contrast, we observe a decrease in the price coming along with a higher correlation for out-of-the-money options (figure (6.3)). 

Now, comparing the non-differentiable RF model with the integrated T-differentiable counterpart, we find the similar partially offsetting volatility effects. Interestingly, now the price of an in-the-money option given anon-differentiable RF is lower that the price of the T-differentiable counterpart and vice verca (see figure (6.4)). Note that the two different RF models coincide for 7 = 0 and 7= < . 

The continuously compounded constant spot rate is r as before. An investor has a choice of purchasing the zero-coupon bond at price P(t, T), which will return the sum of 1 at time T, or of investing this same amount of cash in the money market account, and this sum would have grown to 1 at time T. We know that the value of the money market accoxmt is given by Me If M must have a... 

If the same amount of cash that could be used to buy the bond at t, invested in the money market account, does not return 1 then arbitrage opportunities will result. If the price of the bond exceeded the discoxmt function then... 

In other words, the option is valuable when the principal is lower than 100. When the inflation rate drops and the economy is in a hypothetical deflation scenario, the option is in the money. This increases the value of an inflation-linked bond. Note that the probability of a deflation scenario depends on the market sentiment and implied inflation rate between conventional and... 

For instance, at maturity, the stock price can have a maximum value of 11.51 and a minimum value of 0.35, according to the assumed volatility. Therefore, at higher node, the value of option will be equal to 8.91 as the difference between the stock price of 11.51 and conversion price or strike price of 2.6. In contrast, at lower node, because the stock price of 0.35 is lower than conversion price of 2.6, the option value will be equal to 0. Particular situation is in the middle of the binomial tree in which in the upstate the stock price is 2.84 and downstate is 1.41, meaning that in the first case the option is in the money, while in the second case is out of the money. 

Moreover, the volatility input has a different effect depending on if the option is in or out of the money. In fact, the value of the convertible bond is more sensitive to changes in volatility when the option is in the money (price of the tmderlying asset... 

FIGURE 9.15 The value of a convertible bond - Volatility sensitivity for in the money options. 

Conversely, at the lowest node, the hedge ratio is 0 because the option is out of money or 0. This means that in the first case the bond trade like the equity, while in the second case like a conventional bond. Therefore when the share price increases the delta approaches unity, implying that the option is deeply in the money. In contrast, when the share price is low relative to the conversion price, the sensitivity of the convertible and therefore of the embedded option is low. 

Determine the Value of a Callable Bond Since the option is held by the issuer, the option element decreases the value of the bond. Therefore, the value of a callable bond is found as an option-free bond less the option element according to Formula (11.3). For the hypothetical bond, the price is 106.13-2.31 or 103.82. This is shown in Figure 11.11. The binomial tree shows that at maturity the option free and callable bond have the same price, or 100. Before the maturity, if the interest rates go down, the callable bond s values are less than an option-free bond, and in particular when the embedded option is deeply in the money, the callable values equal the strike price according to the caU schedule. Conversely, when the interest rates go up, the option free and callable bonds have the same price. 

Determine the Value of a Putable Bond As exposed in Formula (11.4), the value of a putable bond is the sum of an option-free bond and an embedded put optimi. Therefore, conversely to a callable bond, the embedded option increases the value of the bond. When the option is deeply in the money, the bond matches the values defined in the put schedule. When the option has no value, option free and putable bonds have the same price. The value of our hypothetical putable bond is 106.13 + 0.33 or 106.45. This is illustrated in Figure 11.14. 

This carries on to bank organisation structure. In most banks, the repo desk for bonds is situated in the money markets area, while in others it will be part of the bond division (the author has experience of banks employing each system). Equity repo is often situated as part of the back office settlement or Treasury function. Bank of England, Quarterly Bulletin, February 1997. 

The repo market has allowed the hedge fund to borrow in sterling at a rate below the cost of unsecured borrowing in the money market (4.95%). The repo market maker is overcollateralised by the difference between the value of the bonds (in ) and the loan proceeds (2%). A rise in USD yields or a fall in the USD exchange rate value will adversely affect the value of the bonds, cansing the market maker to be undercollateralised. 

Moneyness—Is the option worth exercising If so, it is said to be in-the-money (ITM). Our call option struck at 98 would be in-the-money if the underlying bond was trading above 98. If the bond were trading below 98, the call would instead be out-of-the-money (OTM). Finally, if the current price of the underlying asset was the same as the strike price, 98 in this example, the option would be at-the-money (ATM). Premium—The amount paid by the buyer of an option is called the premium. This is normally paid up-front. 

An interest rate cap is effectively a call on interest rates. If interest rates exceed the strike rate, the cap expires in-the-money. Just as a put option... 

Take, for example, a borrower who needs protection against unexpected rises in interest rates over the course of a 5-year loan. EURIBOR might be low right now but, in a rising yield-curve environment, may increase significantly over time. For example, 6-month EURIBOR might currently be 2%, but 6-month forward rates may rise to 5% in the last six months of a 5-year loan. A cap struck at 4% would be well out-of-the-money in early periods, but well in-the-money for later periods. 

The net cost of this strategy is 0.82 million, which is the maximum amount the investor can lose if he or she is wrong and bond prices fall. If bond prices stay the same, the net loss is only 0.34 million, as the option bought is in-the-money, and will expire with some intrinsic value that will be returned to the investor. If bond prices rise up to 1.50%, the investor can enjoy the benefit until the 118.00 strike is reached and profits are capped at around 1.2 million. 

If 2-year rates rise sufficiently in 3-years time, the swaption will expire in-the-money, and the investor can exercise the payer s swaption, entering into a second swap as the fixed-rate payer at exactly the same rate as the original swap, for which the investor is the fixed-rate receiver. This second swap exactly offsets the first swap, effectively cancelling the original swap for the last two years of its life. 

A DNT option is a path-dependent digital option. The digital characteristic means that payment at maturity is not dependent on how much the option is in-the-money instead, the payout, if made, is fixed at the outset. The path-dependent characteristic means that market rates throughout the lifetime of the option are monitored, not just on the maturity date. If, at any time, the nnderlying market rate touches (trades at or through) the barrier levels, this triggers the payout at maturity. 

---