Whether those strike prices are in, at, or out of the money will affect the magnitude of the underlying move needed to reach profitability and also determine whether the trade can be profitable if the underlying stock remains unchanged. These factors include the path of price developments and the resulting variation margin flows, as well as changes in the CTD during the term of the transaction. An investor selling an option assumes a short position. The delivery price is derived from the final settlement price, multiplied by the conversion factor plus the accrued interest. With government bond forex markt openingstijden zondag futures we know that the futures price will closely track the price movement of the cheapest-to-deliver (CTD) bond. The discount factor is: 1 1 (0.0363.315) The interest rate needs to be raised to a higher power for remaining lifetimes beyond one year (1.315,.315. Frequently there is also a difference between the remaining lifetime of the futures contracts and the hedging period. When hedging a CTD bond the price factor allows for a good hedge performance provided the shape of the yield curve doesnt alter too much over time. 29 EU-134 Fixed rat_E 18:05 Uhr Seite 30 It follows that the bond most likely to be used for delivery is always the bond with the lowest zero basis futures price the cheapest cash bond to purchase. Alternatively 105.70 106.00 30 ticks loss multiplied by the tick value of one bund future (EUR 10) EUR 300. The futures price will track the price of the deliverable bond that presents the short futures position with the greatest advantage upon maturity.

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Therefore, the Macaulay duration of a bond is dominated by the remaining lifetime of those payments with the highest present value. Result of Closeout Given the previous days settlement price.81, a sale on May 15 at a price.70 also prevailing during the day would only result in a variation margin debit of EUR 1,100 (0.11 10 EUR 1,000). I hope this enhanced your understanding of options. A nominal value of 100 Lifetime and Remaining Lifetime One must differentiate between lifetime and remaining lifetime in order to understand fixed income bonds and related derivatives. Changed Market Situation 10-year yields have risen by twenty basis points, compared to ten basis points in the 5-year sector by the beginning of June. There is no assurance that a portfolio will achieve its investment objective. This type of strategy is directed at varying yield developments in the respective maturity sectors. Volatility of the Underlying Instrument Volatility measures the propensity of price fluctuations in the underlying instrument. In general, neither the issue price nor the traded price of a bond corresponds to its nominal value. The hedge ratio is determined as follows using the nominal value method: Hedge ratio Nominal value of the bond portfolio Nominal value of fixed income futures Nominal value of the bond portfolio Sum of nominal value of the bonds.

53 EU-134 Fixed rat_E 18:05 Uhr Seite 54 Options on Fixed Income Futures Overview The following three option contracts on fixed income futures are currently traded at Eurex: 54 Products Product code Option on the Euro Schatz Future. In the first part of this series, Getting Started With Options, we discussed the basics of options such as terminology, rights and obligations, open interest, pricing, sentiment and expiration cycles. Macaulay Duration (Average Remaining Lifetime Weighted by Present Value). Maximum loss 300 (3.00 option premium paid x 100 shares per contract). Investors incurring losses on their futures positions possibly as a result of incorrect market forecasts are obliged to settle these losses immediately, and in full (variation margin). 47 EU-134 Fixed rat_E 18:05 Uhr Seite 48 The principle of cash-and-carry arbitrage is explained below, using the valuation example taken from the section on futures pricing. These factors work against the owner of a long option, resulting in a much more difficult profit-and-loss scenario than you might think. The most important terms are described in the following example. Explanations of fixed income securities contained in this brochure predominantly refer to such issues on which Eurex fixed income derivatives are based. At a yield of 5 the table records the cash market price at delivery and the zero basis futures price (i.e.

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As previously mentioned, the underlying instruments available for trading are the Euro Bund, Euro Bobl and the Euro Schatz Futures. Profit and Loss Profile on the Last Trading Day, Short Fixed Income Futures 0 Profit and loss Bond price P/L short fixed income futures Rationale The investor wishes to *fixed income options trading strategies* benefit from rising yields, but is unable to sell the actual bonds short (i.e. 3.63 Bond.5 Federal Republic of Germany debt security due on July 10, 2003 Nominal value 100 Coupon.5 100.50 Valuation date July 11, 2002 (today) This results in the following equation 4: Present value Nominal. For example, if you are extremely bullish, you may want to consider out-of-the-money (ootm) long calls or in-the-money (ITM) short puts. Change in value of the option compared to the previous day EUR 1,100 EUR 7,000 EUR 8,100 Option premium to be paid EUR 7,000.70 10 1,000 Variation margin on 05/15/2002 EUR 3,100 Result of the Exercise These. The portfolio may exceed these from time to time due to market conditions and outstanding trades.

Alternatively the __fixed income options trading strategies__ net profit is the sum of the futures price movement multiplied by 10 contracts multiplied by the value of EUR 10: (105.37 105.10) 10 EUR 10 EUR 2,700. Otherwise parallel shifts in the yield curve would lead to a change in the value of the spread. The buyer is prepared to pay a certain sum the time value for this opportunity. Accrued Interest, the Yield Curve Bond Valuation Macaulay Duration Modified Duration Convexity the Tracking Error of Duration Eurex Fixed Income Derivatives Characteristics of Exchange-traded Financial Derivatives Introduction Flexibility Transparency and Liquidity Leverage Effect Introduction to Fixed Income Futures What are Fixed Income Futures? In other words, the substantial profit potential associated with a straight fixed income future position is reflected by the significant risks involved. The simultaneous establishment of long and short positions is subject to lower risks compared to outright long or short positions.

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Futures Positions Obligations A futures position can either be long or short: Long position Buying a futures contract Short position Selling a futures contract The buyers obligations: At maturity, a long position automatically results in the obligation to **fixed income options trading strategies** buy. Investors must weigh up the costs and benefits of an adjustment. Bonds are categorized according to their lifetime, issuer, interest payment details, credit rating and other factors. Spread positions are designed to achieve profits on expected changes in the price difference between the long and short positions. The following rule applies to describe the relationship between the present value or the clean price of a bond and interest rate developments: Bond prices and market yields react inversely to one another. In case the delivery price of a bond is higher than its market valuation, holders of a short position can make a profit on the delivery, by buying the bond at the market price and selling it at the higher delivery price. Only the Confederation Bonds with different lifetimes are freely tradable. Maximum gain 4,700 (50 strike price.00 option premium x 100 shares per contract). Identifying the CTD under different market conditions CTD 7 05/13/2011 CTD 5 07/15/2012 106.92 100.00.72 5 Zero basis futures price Market yield 6 7 5 07/15/ /13/2011 31 EU-134 Fixed rat_E 18:05 Uhr Seite 32 Applications of Fixed. Hedging means securing the price of an existing or planned portfolio. The futures price can also be expressed as follows 8: Price of the deliverable bond Futures price Cost of carry The basis is the difference between the bond price in the cash market (expressed by the prices of deliverable.

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Electronic trading on Eurex guarantees extensive transparency of prices, volumes and executed transactions. So, if market yields are below the implied discount rate (i.e. Or to sell Put option Calls Puts. For a futures position, contrary to investing on the cash market, only additional margin needs to be pledged (cf. To do this, the portfolio would be slightly more heavily weighted towards the two-year bond. In general, however, the price /yield relationship of bonds tends to be convex, and therefore, a price increase calculated by means of the modified duration is under- or overestimated, respectively. The variation margin calculation results in the following: Example Euro Bund variation margin: EUR 105,700 (105.70 of EUR 100,000) EUR 106,000 (106.00 of EUR 100,000) EUR 300 The buyer of the Euro Bund Futures incurs a loss. Offsetting long and short positions in different maturity months of the same futures contract are referred to as spread positions. Any views and opinions provided are those of the portfolio management team and are subject to change at any time due to market or economic conditions and may not necessarily come to pass. For instance, futures are designed to track the price development of the underlying instrument during the lifetime of the contract. 57 EU-134 Fixed rat_E 18:05 Uhr Seite 58 Important Risk Parameters Greeks An options price is affected by a number of parameters, principally changes in the underlying price, time and volatility. The closer it moves towards expiration, the lower the time value and hence the lower the option price ceteris paribus. Date Transaction Purchase/ selling price Daily settlement price 03/11 Buy 10 Euro Bobl Futures June 2002 105.10 104.91 Variation margin 10 profit in EUR 03/12 104.97 03/13 104.80 03/14 104.69 03/15 104.83 1,400 03/18 105.14 3,100 03/19 105.02.

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The profit and loss calculation for the sale of the option is shown below: Date Transaction Purchase/ selling in EUR **fixed income options trading strategies** Option daily settlement price in EUR Variation margin profit in EUR 05 /15 Sale.70 Variation margin. To help standardize the delivery process the concept of a notional bond is used. Typically, the longer it is until the bond matures, the higher its return will. 49 EU-134 Fixed rat_E 18:05 Uhr Seite 50 Buyers and sellers of options on fixed income futures have the following rights and obligations: Call option Put option Call buyer Call seller Put buyer Put seller Long. To provide a better understanding of the contracts described, the fundamental characteristics of fixed income securities and the indicators used to analyze them will be outlined. In other words the premium is not fully paid until the option expires or is exercised.

Rationale An investor analyzes the value of the September 2002 Euro Bobl Future in April and establishes that the contract is overvalued. Eurex lists futures and options on financial instruments. In comparison to outright position trading, inter-product spreads are also subject to lower risks. Long puts, similar to a long call trade, a long put trade is fairly straightforward. The investor buys 10 put options on this contract with an exercise price of 106.00. An option position on fixed income futures can be liquidated by closing it out (see below the buyer of the option can also close it by exercising the option. Fixed income bonds bear a fixed interest payment, known as the coupon, which is based on the nominal value of the bond. Zero basis futures price at 5, 6, 7 yield Coupon Maturity 5 07/15/2012.925836.99 107.99.58.54 107.58.97 7 05/13/2011.12 106.92 106.75 100.01 Conversion factor Price at 5 Price.

7 EU-134 Fixed rat_E 18:05 Uhr Seite 8 In this chapter the following information will be used for a number of explanations and calculations: Example: Debt security issue German Government Bond. Basic knowledge of the securities industry is a prerequisite. An option holder wishing to exercise his/her right must inform the clearing house, which in turn nominates a short position *fixed income options trading strategies* holder by means of a neutral random assignment procedure. There is no guarantee that any investment strategy will work under all market conditions, and each investor should evaluate their ability to invest for the long-term, especially during periods of downturn in the market. Pairing stocks and options Source: Schwab Center for Financial Research. The other advantage of the butterfly is that if the relationship in yields changes, it could increase returns. This is also referred to as compounding the interest. The additional margin pledged is released the following day. The Macaulay duration indicator was developed to analyze the interest rate sensitivity of bonds, or bond portfolios, for the purpose of hedging against unfavorable interest rate changes. The following section outlines the most common procedures. These are included in the appendices.

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A basic butterfly trade consists of buying and selling three different terms of a given bond. To profit on a long call trade, you will __fixed income options trading strategies__ need to be right about the direction of the underlying stock price movement and the number of points it moves in that direction, as well as how long it takes to make the move. Basis Convergence (Schematic) Negative Cost of Carry Positive Cost of Carry Price Time Price of the deliverable bond Futures price The following relationships apply: Financing costs Proceeds from the cash position: Negative cost of carry Financing costs Proceeds from. This means that long-term yields will rise more (or fall less) than medium-term yields. The short fixed income futures diagram illustrates the outcome of the futures price and its corresponding profit and loss potential. Other government bonds are exchanged only between the SNB and banks, or in interbank trading. A nominal value of 100. With a lifetime of 10 years. Time value Option price Intrinsic value 55 EU-134 Fixed rat_E 18:05 Uhr Seite 56 Determining Factors The theoretical price of options on fixed income futures can be calculated using different parameters, regardless of the current supply and demand scenario. This additional margin deposit is designed to protect the clearing house against a forward adverse price movement in the futures contract. The following example outlines how the option price reacts to a change in volatility.

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Likewise, sellers demand a higher return to cover their increasing risks. In order to estimate the changes in an options price, a series *fixed income options trading strategies* of sensitivities are used, which are known as the Greeks. Therefore the profit on the one futures trade is 15 CHF 10 1 CHF 150. The coupon and the nominal value are repaid at maturity. Due to the different interest rate sensitivities of the respective issues, the medium-term and long-term positions are weighted differently.

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To enter an uncovered call trade, youll need the __fixed income options trading strategies__ highest option approval level available at Schwab (level 3 and must have substantial funds to meet the higher margin requirements of this strategy. 27 EU-134 Fixed rat_E 18:05 Uhr Seite 28 Example: Trade date May 3, 2002 Value date May 8, 2002 Cheapest-to-deliver bond.75 Federal Republic of Germany debt security due on January 4, 2011 Price of the cheapest-to-deliver.50 Futures. The following fundamental relationships describe the characteristics of Macaulay duration: Macaulay duration is lower, the shorter the remaining lifetime; the higher the market interest rate; and the higher the coupon. When disproportionate shifts occur, the investor can earn a net return. Chapters Macaulay Duration and Modified Duration. Gamma can thus be used to recalculate delta. The greater the volatility, the higher the option price. The contracts were bought at a price of 121.50. This corresponds to the volatility reflected in a current market option price. Additional margin is released to the investor. Buying a basket of bonds with a method called a butterfly, allows you to speculate on certain changes in the relationship between the returns of short-term and long-term bonds. If a change in the yield curve results in a change in the status of the CTD bond during the life of the hedge, then the success of the futures hedge may be affected.

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However, its good to discuss the strategy because it helps to lay the foundation for more complex option strategies. Long put The buyer of a put has the right, but not the obligation, to sell the futures contract at an exercise price agreed in advance. The change in value relative to the capital invested is consequently much higher than for a similar cash market transaction. Keep in mind, both will generally require a bullish move in the underlying stock of extreme magnitude in order to reach profitability. Source: Schwab Center for Financial Research. It is not possible to invest directly in an index. The interest accrued from the last coupon payment date up to the valuation date is referred to as the accrued interest. Chapter Conversion Factor and Cheapest-to-Deliver Bond. When calculating additional margin, the correlation of the price development is taken into account by the fact that the Euro Bund and the Euro Bobl Futures form part of the same margin group. Conversely, the longer the lifetime the higher the risk for the option seller, calling for a higher price for the option. The closer an option moves towards expiration, the lower the time value becomes until it eventually reaches zero on that date.

Please consider the investment objectives, risks and fees of the Strategy carefully before investing. Arbitrage is exploiting price imbalances **fixed income options trading strategies** to achieve risk-free profits. An investor buys: 2 Contracts The futures transaction is based on a nominal value of 2 x EUR 100,000 of deliverable bonds for the Euro Bund Future, or 2 x CHF 100,000 of deliverable bonds for the conf Future. The following section illustrates the determining factors of time value. However, it is worth noting that when entering into a futures position it is not necessarily based upon the intention to actually deliver, or take delivery of, the underlying instruments at maturity. As we pointed out above, this bias is caused by theincorrect discount rate of 6 percent implied by the way the conversion factor is calculated. Bearish options strategies Source: Schwab Center for Financial Research. This is referred to as an assignment of the short position. Determining the Hedge Ratio The relationship of the futures position to the portfolio in other words, the number of futures contracts required for the hedge is referred to as the hedge ratio. The information presented represents how the portfolio management team generally implements its investment process under normal market conditions. A cross hedge involves strategies where for the reasons outlined above the hedge position does not precisely offset the performance of the hedged portfolio.

By paying the option price (the premium) the buyer of an option acquires the right, for example. Longer-term securities may be more sensitive to interest rate changes. Please note you've to add our email to approved e-mail addresses. Trading involves entering into positions on the derivatives market for the purpose of making a profit, assuming that market developments are forecast correctly. Using the modified duration method, the hedge ratio is calculated as follows: Hedge ratio Market value of the bond portfolio Modified duration of the bond portfolio Conversion factor Price (CTD) 1,000 Modified duration (CTD) This method is limited. Given the contract specifications, only integer multiples of a futures contract may be traded. This bond is called the cheapest to deliver (or CTD). Gamma can be described as the rate of change of delta. Long call, source: Schwab Center for Financial Research. This obligation is valid until the options expiration date. The modified duration is equivalent to the negative value of the Macaulay duration, discounted over a period of time: Modified duration Duration 1 Yield The modified duration for the example above is: Modified duration.65.38.0363 According.