Amortizing and Accreting Swap Valuation Introduction and Practical Guide
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An amortizing swap is an interest rate swap whose notional principal amount declines during the life of the contract whereas an accreting swap is an interest rate swap whose notional principal amount increases instead. The notional amount changes could be one leg or two legs, but typically on a fixed schedule. The notional principal is tied to an underlying financial instrument with a declining principal, such as a mortgage or an increasing principal, such as a construction fund. The notional principal of an amortizing swap is tied to an underlying financial instrument with a declining principal, such as a mortgage. On the other hand, the notional amount of an accreting swap is tied to an underlying instrument with an increasing principal, such as a construction fund. The notional principal schedule of an amortizing or an accreting swap may decrease or increase at the same rate as the underlying instrument. Both amortizing and accreting swaps can be used to reduce or increase exposure to fluctuations in interest rates. This presentation gives an overview of amortizing or accreting swap product and valuation model.
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4) Selecting a growth pattern such as stable, two-stage, or three-stage based on the firm's growth characteristics and life cycle stage.
15. forex_M&A.pptx
The document discusses foreign exchange rates and mergers and acquisitions. It defines exchange rates as the price of one currency in terms of another currency. Exchange rates can be quoted in both directions between two currencies, such as dollars to euros or euros to dollars. The document also discusses spot rates for immediate delivery and forward rates for future delivery. Mergers can be horizontal between competitors, vertical between companies in different production stages, or conglomerate. Mergers aim to reduce costs through economies of scale or gain control over the production process through vertical integration. Mergers and acquisitions seek to create shareholder value through returns higher than the cost of capital.
The analysis and valuation of bonds copy
The document discusses the fundamentals of bond valuation and analysis. It defines key terms like nominal yield, current yield, promised yield to maturity, and realized (horizon) yield. It also covers how to compute these yields using present value models and formulas. The document also discusses how interest rates are determined based on supply and demand factors like inflation expectations, risk premiums, and economic conditions. Bond yields are influenced not just by broader interest rate determinants but also issue-specific characteristics that impact risk.
Future Worth method
The document discusses several time value of money concepts:
1) The future worth method calculates the equivalent value of an investment at the end of its period. For example, building a nuclear power plant requires calculating its worth at commercialization.
2) Using the future worth method, investments are accepted if their future worth is positive, rejected if negative, and indifference if zero.
3) The formula for computing future worth considers cash inflows and outflows over the investment period.
4) Bond valuation determines a bond's fair value by calculating the present value of future interest payments and face value at maturity. This yields the required rate of return.
Npv and irr
This document discusses techniques for evaluating investment projects, focusing on net present value (NPV) analysis. It provides the formula for calculating NPV and explains how to use NPV to evaluate projects. It also discusses other methods like internal rate of return (IRR) and profitability index (PI). The document notes some limitations of these techniques and provides guidance on how to address factors like mutually exclusive projects, capital rationing, and risk when evaluating capital budgeting decisions.
Capital budgeting
The document discusses various capital budgeting techniques for evaluating investment projects. It outlines steps for estimating cash flows, including determining net cash outflows, annual cash flows, and final year cash flows. It then explains several evaluation techniques like average rate of return, payback period, discounted payback period, net present value, internal rate of return, and profitability index. The techniques consider factors like time value of money, risk, and whether the technique is consistent with maximizing shareholder wealth. NPV is highlighted as the preferred technique, though others provide supplementary insights into risk, costs, and returns.
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Pricing Puttable Bond
A puttable bond is a bond in which the investor has the right to sell the bond back to the issuer at specified times for a specified price. At each puttable date prior to the bond maturity, the investor may get the investment money back by selling the bond back to the issuer. The underlying bonds can be fixed rate bonds or floating rate bonds. A puttable bond can therefore be considered a vanilla underlying bond with an embedded Bermudan style option. Puttable bonds protect investors. Therefore, a puttable bond normally pays investors a lower coupon than a non-callable bond.
Although a puttable bond is a higher cost to the investor and an uncertainty to the issuer comparing to a regular bond, it is actually quite attractive to both issuers and investors. For investors, puttable bonds allow them to reduce interest costs at a future date should rate increase. For issuers, puttable bonds allow them to pay a lower interest rate of return until the bonds are sold back. If interest rates have increased since the issuer first issues the bond, the investor is like to call its current bond and reinvest it at a higher coupon. This presentation gives an overview of puttable bond and valuation model.
Valuing Callable Bond
A callable bond is a bond in which the issuer has the right to call the bond at specified times from the investor for a specified price. At each callable date prior to the bond maturity, the issuer may recall the bond from its investor by returning the investor’s money. The underlying bonds can be fixed rate bonds or floating rate bonds. A callable bond can therefore be considered a vanilla underlying bond with an embedded Bermudan style option. Callable bonds protect issuers. Therefore, a callable bond normally pays the investor a higher coupon than a non-callable bond.
Although a callable bond is a higher cost to the issuer and an uncertainty to the investor comparing to a regular bond, it is actually quite attractive to both issuers and investors. For issuers, callable bonds allow them to reduce interest costs at a future date should rate decrease. For investors, callable bonds allow them to earn a higher interest rate of return until the bonds are called off. This presentation gives an overview of callable bond and valuation model.
Valuing Interest Rate Futures Options
This document discusses interest rate future options. It defines interest rate future options as options that give the holder the right to buy or sell an interest rate future contract at a specified price on a specified date. It notes some advantages of trading these options, such as speculation and leverage. It then discusses models for valuing these options, including the Black-Scholes model and binomial trees. Finally, it provides a real-world example of an interest rate future option specification.
Valuing Interest Rate Futures
An interest rate future is a futures contract between the buyer and seller to deliver an interest bearing asset, that allows the buyer and seller to lock in the price of the interest bearing asset for a future date.
Interest rate futures are used to hedge against interest rate risk. Investors can use Eurodollar futures to secure an interest rate for money it plans to borrow or lend in the future. This presentation gives an overview of interest rate future product and pricing model. You find more presentations at http://www.finpricing.com/productList.html
Cancelable Swap Valuation and Risk
A cancelable swap provides the right but not the obligation to cancel the interest rate swap at predefined dates. Most commonly traded cancelable swaps have multiple exercise dates. Given its Bermudan style optionality, a cancelable swap can be represented as a vanilla swap embedded with a Bermudan swaption. Therefore, it can be decomposed into a swap and a Bermudan swaption. Most Bermudan swaptions in a bank book actually come from cancelable swaps.
Cancelable swaps provide market participants flexibility to exit a swap. This additional feature makes the valuation complex. This presentation provides practical details for pricing cancelable swaps.
Bermudan Swaption Valuation
An interest rate Bermudan swaption gives the holder the right but not the obligation to enter an interest rate swap at predefined dates. It is one of the fundamental ways for an investor to enter a swap. Comparing to regular swaptions, Bermudan swaptions provide market participants more flexibility and control over the exercising of an option and less restriction.
Given those flexibilities, a Bermudan swaption is more expensive than a regular European swaption. In terms of valuation, it is also much more complex. This presentation provides practical details for pricing cancelable swaps.
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financial assets represent claim for future benefit or cash. Financial assets are formed by establishing contracts between participants. These financial assets are used for collection of huge amounts of money for business purposes.
Two major Types: Debt Securities and Equity Securities.
Debt Securities are Also known as fixed-income securities or instruments. The type of assets is formed by establishing contracts between investor and issuer of the asset.
• The first type of Debit securities is BONDS. Bonds are issued by corporations and government (both local and national government).
• The second important type of Debit security is NOTES. Apart from similarities associated with notes and bonds, notes have shorter term maturity.
• The 3rd important type of Debit security is TRESURY BILLS. These securities have short-term ranging from three months, six months, and one year. Issuer of such securities are governments.
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There are no fixed maturity dates in such securities, and asset’s value is determined by company’s performance. There are two major types of equity securities: common stock and preferred stock.
Common Stock: These are simple equity securities and bear no complexities which the preferred stock bears. Holders of such securities or instrument have the voting rights when it comes to select the company’s board of director or the business decisions to be made.
Preferred Stock: Preferred stocks are sometime referred to as hybrid securities, because it contains elements of both debit security and equity security. Preferred stock confers ownership rights to security holder that is why it is equity instrument
<a href="https://www.writofinance.com/equity-securities-features-types-risk/" >Equity securities </a> as a whole is used for capital funding for companies. Companies have multiple expenses to cover. Potential growth of company is required in competitive market. So, these securities are used for capital generation, and then uses it for company’s growth.
Concluding remarks
Both are employed in business. Businesses are often established through debit securities, then what is the need for equity securities. Companies have to cover multiple expenses and expansion of business. They can also use equity instruments for repayment of debits. So, there are multiple uses for securities. As an investor, you need tools for analysis. Investment decisions are made by carefully analyzing the market. For better analysis of the stock market, investors often employ financial analysis of companies.
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Amortizing and Accreting Swap Valuation Introduction and Practical Guide
- 1. Amortizing and Accreting Swap Vaulation Pratical Guide Alan White FinPricing http://www.finpricing.com
- 2. Amortizing Swap Summary ◆ Interest Rate Amortizing or Accreting Swap Introduction ◆ The Use of Amortizing or Accreting Swap ◆ Valuation ◆ Practical Notes ◆ A real world example
- 3. Amortizing Swap Amortizing or Accreting Swap Introduction ◆ An amortizing swap is an interest rate swap whose notional principal amount declines during the life of the contract ◆ An accreting swap is an interest rate swap whose notional principal amount increases instead. ◆ The notional amount changes could be one leg or two legs, but typically on a fixed schedule. ◆ The notional principal is tied to an underlying financial instrument with a declining principal, such as a mortgage or an increasing principal, such as a construction fund.
- 4. Amortizing Swap The Use of Amortizing or Accreting Swap ◆ The notional principal of an amortizing swap is tied to an underlying financial instrument with a declining principal, such as a mortgage. ◆ On the other hand, the notional amount of an accreting swap is tied to an underlying instrument with an increasing principal, such as a construction fund. ◆ The notional principal schedule of an amortizing or an accreting swap may decrease or increase at the same rate as the underlying instrument. ◆ Both amortizing and accreting swaps can be used to reduce or increase exposure to fluctuations in interest rates.
- 5. Amortizing Swap Valuation ◆ The analytics is similar to a vanilla interest rate swap but the principal amount used by each period may be different. ◆ The present value of a fixed rate leg is given by 𝑃𝑉𝑓𝑖𝑥𝑒𝑑 𝑡 = 𝑅 𝑁𝑖 𝜏𝑖 𝐷𝑖 𝑛 𝑖=1 where t is the valuation date and 𝐷𝑖 = 𝐷(𝑡, 𝑇𝑖) is the discount factor. ◆ The present value of a floating leg is given by 𝑃𝑉𝑓𝑙𝑜𝑎𝑡 𝑡 = 𝑁𝑖 𝐹𝑖 + 𝑠 𝜏𝑖 𝐷𝑖 𝑛 𝑖=1 where 𝐹𝑖 = 𝐷 𝑖−1 𝐷 𝑖 − 1 /𝜏𝑖 is the simply compounded forward rate and s is the floating spread.
- 6. Amortizing Swap Valuation (Cont) ◆ The present value of an interest rate swap can expressed as ◆ From the fixed rate payer perspective, 𝑃𝑉 = 𝑃𝑉𝑓𝑙𝑜𝑎𝑡 − 𝑃𝑉𝑓𝑖𝑥𝑒𝑑 ◆ From the fixed rate receiver perspective, 𝑃𝑉 = 𝑃𝑉𝑓𝑖𝑥𝑒𝑑 − 𝑃𝑉𝑓𝑙𝑜𝑎𝑡
- 7. Amortizing Swap Practical Notes ◆ First of all, you need to generate accurate cash flows for each leg. The cash flow generation is based on the start time, end time and payment frequency of the leg, plus calendar (holidays), business convention (e.g., modified following, following, etc.) and whether sticky month end. ◆ We assume that accrual periods are the same as reset periods and payment dates are the same as accrual end dates in the above formulas for brevity. But in fact, they are different due to different market conventions. For example, index periods can overlap each other but swap cash flows are not allowed to overlap. ◆ The accrual period is calculated according to the start date and end date of a cash flow plus day count convention
- 8. Amortizing Swap Practical Notes (Cont) ◆ The forward rate should be computed based on the reset period (index reset date, index start date, index end date) that are determined by index definition, such as index tenor and convention. it is simply compounded. ◆ Sometimes there is a floating spread added on the top of the floating rate in the floating leg. ◆ The formula above doesn’t contain the last live reset cash flow whose reset date is less than valuation date but payment date is greater than valuation date. The reset value is 𝑃𝑉𝑟𝑒𝑠𝑒𝑡 = 𝑟0 𝑁𝜏0 𝐷0 where 𝑟0 is the reset rate.
- 9. Amortizing Swap Practical Notes (Cont) ◆ The present value of the reset cash flow should be added into the present value of the floating leg. ◆ Some dealers take bid-offer spreads into account. In this case, one should use the bid curve constructed from bid quotes for forwarding and the offer curve built from offer quotes for discounting.
- 10. Amortizing Swap A Real World Example Fixed Leg Specification Floating Leg Specification Notional Schedule Currency USD Currency USD 6100520 9/1/2015 Day Count dcAct360 Day Count dcAct360 6075492 10/1/2015 Leg Type Fixed Leg Type Float 6050464 11/1/2015 Notional 6100520 Notional 6100520 6024284 12/1/2015 Pay Receive Receive Pay Receive Pay 5998104 1/1/2016 Payment Frequency 1M Payment Frequency 1M 5971924 2/1/2016 Start Date 9/1/2015 Start Date 9/1/2015 5945744 3/1/2016 End Date 4/3/2023 End Date 4/3/2023 5919564 4/1/2016 Fixed Rate 0.0245 Spread 0 5893384 5/1/2016 Index Specification 5867204 6/1/2016 Index Type LIBOR 5841024 7/1/2016 Index Tenor 1M 5814844 8/1/2016 Index DayCount dcAct360 5788664 9/1/2016
- 11. Thanks!