Pricing Puttable Bond
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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.
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Ib0018 – export import finance
Dear students get fully solved assignments
Send your semester & Specialization name to our mail id :
“ help.mbaassignments@gmail.com ”
or
Call us at : 08263069601
(Prefer mailing. Call in emergency )
Notes for Volatility Modeling lectures, Antoine Savine at Copenhagen University
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2) It introduces Black-Scholes option pricing theory, describing how Black-Scholes derives the partial differential equation for option prices and provides a unique solution through arbitrage arguments.
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This document provides an overview of currency derivatives, including forward contracts, futures contracts, and options contracts. It explains how these instruments work and how they can be used by multinational corporations and speculators to hedge currency risk or speculate on anticipated exchange rate movements. Forward contracts lock in an exchange rate for a future date, while futures contracts standardize the amount and settlement date. Options contracts provide the right but not obligation to buy or sell a currency at a set price. These derivatives allow risk from currency fluctuations to be transferred between parties.
กลยุทธ์การซื้อขายสินค้าเกษตรล่วงหน้า
This document discusses strategies for pricing and hedging agricultural commodities. It covers pricing models using concepts like convenience yield and storage costs. It also discusses basis risk, hedging techniques including direct and cross hedging, and estimating hedge ratios. Additional topics include spread trading, using seasonal patterns, and forecasting techniques involving fundamental and technical analysis. The strategies aim to manage risk for those involved in agricultural commodity markets.
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
4_RealOptions.pdf
Objectives
• Know that standard NPV analysis does not account for real options
• Basic understanding of option pricing
– Black-Scholes formula
– Binomial model
• Know different types of real options and their implications
– Option to Expand
– Option to Wait
• Improve your ability to recognize valuable real options to make good business decisions
payoffoptions2-191030161254.pptx
This document discusses various financial derivatives contracts including futures, forwards, and options. It provides terminology related to these contracts such as payoff, strike price, expiration date, and types of options. It explains the difference between futures and forward contracts. Futures contracts are exchange-traded and standardized, while forwards are over-the-counter agreements between two parties. Advantages of forward contracts include no upfront fees and complete hedging of currency risk, while disadvantages are requirement of tying up capital and default risk.
Amortizing and Accreting Swap Valuation Introduction and Practical Guide
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.
Applications of Machine Learning in High Frequency Trading
Machine learning techniques can be applied to high frequency trading by developing predictive models from large datasets capturing market microstructure features at fine granularities. However, this presents challenges due to the lack of understanding how low-level data relates to trading outcomes and lack of intuitions about how order book distributions impact prices. The study compares various machine learning strategies applied to data from Bloomberg Terminal to design an effective high frequency trading strategy.
Future and Forward
Forward and futures contracts allow parties to lock in a price today for buying or selling an asset in the future. Futures contracts are traded on exchanges and have features like margin requirements and marking to market that reduce default risk. Both can be used for hedging to reduce price risk or for speculating to profit from price changes, with futures generally having lower upfront costs but potential for larger losses than options.
35 page the term structure and interest rate dynamics
The document discusses theories and models of the term structure of interest rates. It covers spot and forward rates, the swap rate curve, traditional theories like expectations theory and liquidity preference theory, modern term structure models like CIR and Vasicek, yield curve factor models, and measures of sensitivity to shifts in the yield curve like duration.
Interest Rate Swap Valuation Introduction and Practical Guide
An interest rate swap is an agreement between two parties to exchange future interest rate payments over a set period of time. It consists of a series of payment periods, called swaplets. The most popular form of interest rate swaps is the vanilla swaps that involve the exchange of a fixed interest rate for a floating rate, or vice versa. There are two legs associated with each party: a fixed leg and a floating leg. Swaps are OTC derivatives that bear counterparty credit risk beside interest rate risk.
Interest rate swaps are the most popular OTC derivatives that are generally used to manage exposure to fluctuations in interest rates. Swaps can be also used to obtain a marginally lower interest rate. Thus they are often utilized by a firm that can borrow money easily at one type of interest rate but prefers a different type. They also allow investors to adjust interest rate exposure and offset interest rate risks. Speculators use swaps to speculate on the movement of interest rates. More and more swaps are cleared through central counterparties nowadays (CCPs). This presentation gives an overview of interest rate swap product and valuation model.
Derivative - Forward and future contract
This document provides an overview of derivative contracts, specifically forward and future contracts. It defines derivatives and describes how forward contracts are bilateral agreements between two parties to buy or sell an asset at a future date for a predetermined price. Future contracts are similar to forwards but are standardized and exchange-traded. The key differences between forwards and futures highlighted are that futures are traded on exchanges, require margin payments, follow daily settlement marked to market, and can be closed prior to delivery, whereas forwards are customized OTC contracts.
The reversal rate - Banquedefrance
- The document discusses the concept of a "reversal interest rate", which is the rate at which further monetary policy interest rate cuts become contractionary rather than accommodative, possibly due to financial instability.
- It examines how the reversal rate is determined by factors such as market structure, funding structure, banks' equity levels, interaction with prudential regulation, and other macroprudential policies.
- Using a one period model, it analyzes how interest rate cuts affect bank profits and lending, showing that a constraint on lending can cause the reversal rate to be higher than in an unconstrained monopoly model.
Similar to Pricing Puttable Bond (20)
Amortizing and Accreting Swap Valuation Introduction and Practical Guide
Amortizing and Accreting Swap Valuation Introduction and Practical Guide
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Independent Study - College of Wooster Research (2023-2024)
"Does Foreign Direct Investment Negatively Affect Preservation of Culture in the Global South? Case Studies in Thailand and Cambodia."
Do elements of globalization, such as Foreign Direct Investment (FDI), negatively affect the ability of countries in the Global South to preserve their culture? This research aims to answer this question by employing a cross-sectional comparative case study analysis utilizing methods of difference. Thailand and Cambodia are compared as they are in the same region and have a similar culture. The metric of difference between Thailand and Cambodia is their ability to preserve their culture. This ability is operationalized by their respective attitudes towards FDI; Thailand imposes stringent regulations and limitations on FDI while Cambodia does not hesitate to accept most FDI and imposes fewer limitations. The evidence from this study suggests that FDI from globally influential countries with high gross domestic products (GDPs) (e.g. China, U.S.) challenges the ability of countries with lower GDPs (e.g. Cambodia) to protect their culture. Furthermore, the ability, or lack thereof, of the receiving countries to protect their culture is amplified by the existence and implementation of restrictive FDI policies imposed by their governments.
My study abroad in Bali, Indonesia, inspired this research topic as I noticed how globalization is changing the culture of its people. I learned their language and way of life which helped me understand the beauty and importance of cultural preservation. I believe we could all benefit from learning new perspectives as they could help us ideate solutions to contemporary issues and empathize with others.
Bridging the gap: Online job postings, survey data and the assessment of job ...
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OJP data from firms like Vicinity Jobs have emerged as a complement to traditional sources of labour demand data, such as the Job Vacancy and Wages Survey (JVWS). Ibrahim Abuallail, PhD Candidate, University of Ottawa, presented research relating to bias in OJPs and a proposed approach to effectively adjust OJP data to complement existing official data (such as from the JVWS) and improve the measurement of labour demand.Who Is the Largest Producer of Soybean in India Now.pdf
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Earn a passive income with prosocial investing
Invest in prosocial funds that earn you an income while improving the world
一比一原版(GWU,GW毕业证)加利福尼亚大学|尔湾分校毕业证如何办理
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国外毕业证学位证成绩单如何办理：
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The Rise of Generative AI in Finance: Reshaping the Industry with Synthetic Data
In this presentation, we will explore the rise of generative AI in finance and its potential to reshape the industry. We will discuss how generative AI can be used to develop new products, combat fraud, and revolutionize risk management. Finally, we will address some of the ethical considerations and challenges associated with this powerful technology.
一比一原版(IC毕业证)帝国理工大学毕业证如何办理
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我们从事工作十余年的有着丰富经验的业务顾问，熟悉海外各国大学的学制及教育体系，并且以挂科生解决毕业材料不全问题为基础，为客户量身定制1对1方案，未能毕业的回国留学生成功搭建回国顺利发展所需的桥梁。我们一直努力以高品质的教育为起点，以诚信、专业、高效、创新作为一切的行动宗旨，始终把“诚信为主、质量为本、客户第一”作为我们全部工作的出发点和归宿点。同时为海内外留学生提供大学毕业证购买、补办成绩单及各类分数修改等服务；归国认证方面，提供《留信网入库》申请、《国外学历学位认证》申请以及真实学籍办理等服务，帮助众多莘莘学子实现了一个又一个梦想。
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你做代理，可以改变自己，改变他人，给他人和自己一个机会美景更增添一份性感夹杂着一份纯洁的妖娆毫无违和感实在给人带来一份悠然幸福的心情如果说现在的审美已经断然拒绝了无声的话那么在树林间飞掠而过的小鸟叽叽咋咋的叫声是否就是这最后的点睛之笔悠然走在林间的小路上宁静与清香一丝丝的盛夏气息吸入身体昔日生活里的繁忙与焦躁早已淡然无存心中满是悠然清淡的芳菲身体不由的轻松脚步也感到无比的轻快走出这盘栾交错的小道眼前是连绵不绝的山峦浩荡天地间大自然毫无吝啬的展现它的达
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Falcon stands out as a top-tier P2P Invoice Discounting platform in India, bridging esteemed blue-chip companies and eager investors. Our goal is to transform the investment landscape in India by establishing a comprehensive destination for borrowers and investors with diverse profiles and needs, all while minimizing risk. What sets Falcon apart is the elimination of intermediaries such as commercial banks and depository institutions, allowing investors to enjoy higher yields.
Who Is Abhay Bhutada, MD of Poonawalla Fincorp
Abhay Bhutada, the Managing Director of Poonawalla Fincorp Limited, is an accomplished leader with over 15 years of experience in commercial and retail lending. A Qualified Chartered Accountant, he has been pivotal in leveraging technology to enhance financial services. Starting his career at Bank of India, he later founded TAB Capital Limited and co-founded Poonawalla Finance Private Limited, emphasizing digital lending. Under his leadership, Poonawalla Fincorp achieved a 'AAA' credit rating, integrating acquisitions and emphasizing corporate governance. Actively involved in industry forums and CSR initiatives, Abhay has been recognized with awards like "Young Entrepreneur of India 2017" and "40 under 40 Most Influential Leader for 2020-21." Personally, he values mindfulness, enjoys gardening, yoga, and sees every day as an opportunity for growth and improvement.
This assessment plan proposal is to outline a structured approach to evaluati...
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This assessment plan proposal is to outline a structured approach to evaluati...
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Applying the Global Internal Audit Standards_AIS.pdf
Pricing Puttable Bond
- 1. Puttable Bond and Vaulation Dmitry Popov FinPricing http://www.finpricing.com
- 2. Puttable Bond Summary ◆ Puttable Bond Definition ◆ The Advantages of Puttable Bonds ◆ Puttable Bond Payoffs ◆ Valuation Model Selection Criteria ◆ LGM Model ◆ LGM Assumption ◆ LGM calibration ◆ Valuation Implementation ◆ A real world example
- 3. Puttable Bond Puttable Bond Definition ◆ A puttable bond is a bond in which the investor has the right to sell the bond back to the issuer at specified times (puttable dates) for a specified price (put price). ◆ At each puttable date prior to the bond maturity, the investor may sell the bond back to its issuer and get the investment money back. ◆ 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 pay the investor a lower coupon than a non-callable bond.
- 4. Puttable bond Advantages of Puttable Bond ◆ Although a puttable bond is a lower income 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 put its current bond and reinvest it at a higher coupon.
- 5. Puttable Bond Puttable Bond Payoffs ◆ At the bond maturity T, the payoff of a Puttable bond is given by 𝑉𝑝 𝑡 = 𝐹 + 𝐶 𝑖𝑓 𝑛𝑜𝑡 𝑝𝑡𝑡𝑒𝑑 max(𝑃𝑝, 𝐹 + 𝐶) 𝑖𝑓 𝑝𝑢𝑡𝑡𝑒𝑑 where F – the principal or face value; C – the coupon; 𝑃𝑝 – the call price; min (x, y) – the minimum of x and y ◆ The payoff of the Puttable bond at any call date 𝑇𝑖 can be expressed as 𝑉𝑝 𝑇𝑖 = 𝑉 𝑇 𝑖 𝑖𝑓 𝑛𝑜𝑡 𝑝𝑢𝑡𝑡𝑒𝑑 max 𝑃𝑝, 𝑉 𝑇 𝑖 𝑖𝑓 𝑝𝑢𝑡𝑡𝑒𝑑 where 𝑉 𝑇 𝑖 – continuation value at 𝑇𝑖
- 6. Puttable Bond Model Selection Criteria ◆ Given the valuation complexity of puttable bonds, there is no closed form solution. Therefore, we need to select an interest rate term structure model and a numerical solution to price them numerically. ◆ The selection of interest rate term structure models ◆ Popular interest rate term structure models: Hull-White, Linear Gaussian Model (LGM), Quadratic Gaussian Model (QGM), Heath Jarrow Morton (HJM), Libor Market Model (LMM). ◆ HJM and LMM are too complex. ◆ Hull-White is inaccurate for computing sensitivities. ◆ Therefore, we choose either LGM or QGM.
- 7. Puttable Bond Model Selection Criteria (Cont) ◆ The selection of numeric approaches ◆ After selecting a term structure model, we need to choose a numerical approach to approximate the underlying stochastic process of the model. ◆ Commonly used numeric approaches are tree, partial differential equation (PDE), lattice and Monte Carlo simulation. ◆ Tree and Monte Carlo are notorious for inaccuracy on sensitivity calculation. ◆ Therefore, we choose either PDE or lattice. ◆ Our decision is to use LGM plus lattice.
- 8. Puttable Bond LGM Model ◆ The dynamics 𝑑𝑋 𝑡 = 𝛼 𝑡 𝑑𝑊 where X is the single state variable and W is the Wiener process. ◆ The numeraire is given by 𝑁 𝑡, 𝑋 = 𝐻 𝑡 𝑋 + 0.5𝐻2 𝑡 𝜁 𝑡 /𝐷(𝑡) ◆ The zero coupon bond price is 𝐵 𝑡, 𝑋; 𝑇 = 𝐷 𝑇 𝑒𝑥𝑝 −𝐻 𝑡 𝑋 − 0.5𝐻2 𝑡 𝜁 𝑡
- 9. Puttable Bond LGM Assumption ◆ The LGM model is mathematically equivalent to the Hull-White model but offers ◆ Significant improvement of stability and accuracy for calibration. ◆ Significant improvement of stability and accuracy for sensitivity calculation. ◆ The state variable is normally distributed under the appropriate measure. ◆ The LGM model has only one stochastic driver (one-factor), thus changes in rates are perfected correlated.
- 10. Puttable Bond LGM calibration ◆ Match today’s curve At time t=0, X(0)=0 and H(0)=0. Thus Z(0,0;T)=D(T). In other words, the LGM automatically fits today’s discount curve. ◆ Select a group of market swaptions. ◆ Solve parameters by minimizing the relative error between the market swaption prices and the LGM model swaption prices.
- 11. Puttable Bond Valuation Implementation ◆ Calibrate the LGM model. ◆ Create the lattice based on the LGM: the grid range should cover at least 3 standard deviations. ◆ Calculate the payoff of the puttable bond at each final note. ◆ Conduct backward induction process iteratively rolling back from final dates until reaching the valuation date. ◆ Compare exercise values with intrinsic values at each exercise date. ◆ The value at the valuation date is the price of the puttable bond.
- 12. Puttable Bond A real world example Bond specification Puttable schedule Buy Sell Buy Put Price Notification Date Calendar NYC 100 1/26/2015 Coupon Type Fixed 100 7/25/2018 Currency USD First Coupon Date 7/30/2013 Interest Accrual Date 1/30/2013 Issue Date 1/30/2013 Last Coupon Date 1/30/2018 Maturity Date 7/30/2018 Settlement Lag 1 Face Value 100 Pay Receive Receive Day Count dc30360 Payment Frequency 6 Coupon 0.01
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