Questions and Answers of Derivatives Principles And Practice

Prove the following conditions using an arbitrage argument. In your proof, show the initial positive cash flow when the condition is violated and prove that there are no liabilities at expiration:a.
Prove the following:a. End-of-period conversion value $=X$b. End-of-period reversal value $=-X$c. End-of-period long box spread value $=X_{2}-X_{1}$d. End-of-period short box spread value
Prove mathematically the following condition for the early exercise of a call by a call holder: $D>T V P$.
Suppose just prior to going ex-dividend, XYZ stock is trading at $\$ 65$ and is expected to go ex-dividend with a dividend expected to be worth $\$2.50$ on the ex-dividend date. What advice would
Suppose XYZ stock is trading $\$ 60, X Y Z$ 6o European calls expiring in one year are trading at $\$ 3$, and the annual risk-free rate is $3 \%$. Using the put-call parity model determine the
Suppose XYZ stock is trading at $\$ 60$, XYZ 60 European puts expiring in one year are trading at $\$ 2$, and the annual risk-free rate is $3 \%$. Using the put-call parity model, determine the
Determine the equilibrium price of a December S\&P 500 call, given the S\&P 500 put is trading at 50 . Assume the spot SP 500 index is at 2,500 , the risk-free rate is $5.00 \%$, dividend per index
PI Hedge Fund has formed a proxy portfolio that it is using to identify arbitrage opportunities using put-call parity relations. The proxy portfolio is highly correlated with the S\&P 500 with a beta
Explain what arbitrageurs would do if the price of an American S\&P 500 futures call with an exercise price of 2,100 were priced at 45 when the underlying futures price was trading at 2,150. What
Explain what arbitrageurs would do if the price of an American S\&P 500 futures put with an exercise price of 2,200 were priced at 45 when the underlying futures price was trading at 2,150 . What
Prove the following boundary conditions using an arbitrage argument. In your proof, show the initial positive cash flow when the condition is violated and prove there are no liabilities at expiration
Option price relations can be seen by looking at real-time pricing, market data, and data for exchange-traded call and put options found on OMON, CALL, and PUT. Using the OMON screen for selected a
Use the Chart screen (Chart ) to generate historical prices of a selected stock and its call and put options with different expirations and expiration. Select a period in which the options were
Use the Chart screen (Chart ) to generate historical prices for the S\&P 500 spot, and call and put options on the index with different expirations and expiration. Select a period in which the
Use the Chart screen (Chart ) to generate historical prices for a selected stock and its call and put options with the same expiration and exercise price. Using the "Flag" selection tool (click
Consider a one-period, two-state case in which $\mathrm{ABC}$ stock is trading at $\mathrm{S}_{0}=$ $\$ 100$, has $u$ of 1.10 and $d$ of 0.95 , and the period risk-free rate is $5 \%$.a.
Assume two periods to expiration, $u=1.05, d=1 / 1.05, r_{f}=1.02, S_{0}=\$ 100$, no dividends, and $X=\$ 100$ on a European call expiring at the end of the second period. Find: \(C_{u w}, C_{u
5 10.5 Assume ABC stock price follows a binomial process, is trading at $S_{0}=$ $\$ 100$, has $u=1.10, d=0.95$, and probability of its price increasing in one period is $0.5(q=0.5)$.a. Show
Describe the methodology used to derive the formulas for estimating $u$ and $d$.
Suppose ABC stock has the following prices over the past 13 quarters:a. Calculate the stock's average logarithmic return and variance.b. What is the stock's annualized mean and variance?c. Calculate
Assume a binomial, risk-neutral world where $n=1, \mathrm{~S}_{0}=\$ 100, R_{f}=0.05, u=$ 1.10 , and $d=0.95$.a. What are the risk-neutral probabilities of the stock increasing in one period and
Explain what is meant by risk-neutral pricing. What is the reason for pricing options using a risk-neutral pricing approach?
Consider a one-period, two-state case in which ABC stock is trading at $S_{\mathrm{O}}=$ $\$ 100, u=1.1$, and $d=0.95$, the period risk-free rate is $5 \%$, and the stock is expected to go
ABC stock is trading at $\$ 100$, its annualized standard deviation is $\sigma^{\mathrm{A}}=0.3$, its mean is zero, and its continuous annual dividend yield is $2.5 \%$. The annual risk-free
Using Bloomberg information, estimate the equilibrium price on a call and put option on a selected stock using the BOPM Excel program. Bloomberg option input information:a. Stock price: DES or GP
For one of the options that you evaluated in Exercise 1, evaluate the sensitivity of its binomial option values to different volatilities. Use the HVG screen to help you select the volatilities
Download Bloomberg stock price data from a selected stock's GP screen (right-click your mouse in the graph area; click "Send Data to Clipboard" to download data to Excel). In Excel:a. Calculate
Using the historical volatility and mean you calculated in Exercise 4, select an option on the stock and determine its equilibrium price using the BOPM Excel program. See Exercise 1 for finding input
Suppose XYZ stock currently is trading at $\$ 100$ per share, has an annualized standard deviation of 0.50 , will not pay any dividends over the next three months, and the continuously compounded
Using the continuous-dividend-adjusted option model, calculate the dividend-adjusted stock price, dividend-adjusted call price, and dividend-adjusted put price for the XYZ stock and options described
Discuss the applicability of the pseudo-American model for pricing American call options.
Using the B-S OPM Excel program calculate the call option price for each stock price shown below. Assume $R=3 \%, \sigma=0.50, t=$ 0.25 per year, $X=\$ 100$, and no
Using the B-S OPM Excel program, calculate the call option price for each annualized standard deviation shown below. Assume $R=$ $3 \%, S_{0}=\$ 100, t=0.25, X=\$ 100$, and no
Given the following information on the XYZ stock: $S_{0}=\$ 50, \sigma=$ $0.175, R=3 \%$, and $\beta^{\mathrm{S}}=0.35$, determine the following characteristics of an XYZ 50 European call with
Given the information on the XYZ stock: $S_{0}=\$ 50, \sigma=0.175, R=$ $3 \%, \beta^{\mathrm{S}}=0.35$, and $E\left(R_{\mathrm{S}}\right)=-0.10$, determine the following characteristics of an
Suppose XYZ stock is trading at $\$ 50$, its annualized standard deviation is 0.175 , and the continuously compounded risk-free rate is $6 \%$ (annual).a. Calculate the B-S equilibrium call
Explain the methodology and findings of the following empirical studies, examining the B-S OPM:a. Black-Scholes (1972)b. Galai (1977)c. MacBeth and Merville (1979)
Using Bloomberg's OVME screen, estimate the equilibrium price on a selected call and put option. Guide:- Select the options from the selected stock's OMON or CALL screen.- Load the option: Option
Using the OVME screen for the call and put options you evaluated in Exercise 1, evaluate the prices of the call and put options for different stock prices. Click the "Scenario" tab and set the axis
Create a portfolio of at least two options on the same stock and evaluate the position in terms of the position's OPM value, delta, gamma, and theta. On the OVME screen, click the + icon next to
Using OVME, analyze the profit and stock price relation for different times prior to expiration and expiration for the following option strategies:a. Straddle Purchaseb. Straddle Salec. Bull Call
Create a neutral delta portfolio with two options on the same stock and evaluate the position in terms of the position's OPM value and gamma. On the OVME screen, click the + icon next to "Deals" to
Assume: Current spot S\&P 500 index is at 2,500 , annual risk-free rate $=4 \%$, zero dividends, logarithmic return's annualized mean $=\mu^{\mathrm{A}}=0.10$, and logarithmic return's annualized
Suppose the following:- Spot S\&P 500 is currently at 3,000- Continuous annual dividend yield of $\psi=5 \%$- Annualized standard deviation is $\sigma^{\mathrm{A}}=0.25$- Annual risk-free rate is
Given the following:- The S\&P 500 futures option expiring at the end of 60 days.- The S\&P 500 futures contract expiring at the end of 120 days.- The current spot index is at $S_{0}=3,000$.- The
Given the futures and spot information in Question 3, determine the following option prices using a 30-period binomial tree and the BOPM Excel programs:a. American futures callb. European futures
Determine the price of European futures call with $X=3,000$ using the Black futures option model (Excel model). Show in a table and with a graph the Black futures option model's option prices and
Given the following futures and spot information:- The S\&P 500 futures option expiring at the end of 60 days.- The S\&P 500 futures contract expiring at the end of 60 days.- The current spot index
Assume the following:- Annual risk-free rate on US dollars $=4 \%$.- Annual risk-free rate on British pounds $=2 \%$.- $\$ /$ BP spot exchange rate $=\$1.30 / \mathrm{BP}$.- Mean annualized
Given the following information:- $\sigma^{\mathrm{A}}=0.25$- $R_{f}=4 \%$- Price on crude oil futures expiring in 120 days $=\$ 50$- European call and put options on crude oil futures, each
Mailin Developers is a real estate development company with a project in the Midwest currently valued at $\$ 20$ million. The company financed the project by borrowing from Commerce Bank. The loan
Using Bloomberg's OVME screen, estimate the equilibrium price on a selected call and put spot index option. For information on how to find options from the SECF and how to upload and index options,-
Using the OVME screen for the options you evaluated in Exercise 1 , evaluate the prices of the options for different index prices. Click the "Scenario" tab and set the axis for option prices and
Using Bloomberg's OVME screen, estimate the equilibrium price on a selected call and put futures index. For information on how to find options from the SECF and CTM screens and how to upload the
Using the OVME screen for the call and put option you evaluated in Exercise 4, evaluate the Greeks for different futures prices and time to expiration by clicking the "Scenario" tab and setting the
Create a portfolio of at least two options on the same futures and evaluate the position in terms of the position's OPM value, delta, gamma, and theta. On the OVME screen, click the + icon next to
Using Bloomberg's OV screen, estimate the equilibrium price on a selected call and put currency futures. For information on how to find options from the SECF and CTM screens and how to upload the
Using Bloomberg's OV screen, estimate the equilibrium price on a selected call and put commodity futures. For information on how to find options from the SECF and CTM screens and how to upload the
Determine the equilibrium price on an equity warrant. To search for warrants, go to the SECF screen. On the screen, click "Equities" from the "Category" dropdown, click the "Warrants" tab, and select
Assume: binomial process; current annualized spot rate on riskfree bond with maturity of one year of $S_{0}=5 \%$; up and down parameters for period equal in length to one year of $u=1.1$ and
Assume the following: binomial process; current annualized spot rate on risk-free bond with maturity of 0.25 years of $S_{0}=4 \%$; up and down parameters for period equal in length to 0.5 years of
Assume:- Binomial process- Current annualized spot rate on risk-free bond with maturity of 0.25 years of $S_{0}=4 \%$- Up and down parameters for period equal in length to 0.5 years of \(u=1.1, d=1
Given a current one-period spot rate of $S_{0}=10 \%$, upward and downward parameters of $u=1.1$ and $d=0.9091$, and probability of the spot rate increasing in one period of $q=0.5$ :a.
Given an ABC convertible bond with $F=\$ 1,000$, maturity of three periods, Conversion Ratio $=10$, current stock price of $\$ 100$, and $u=1.1, d=0.95$, and $q=0.5$ on the stock:a.
43%;" height="163">a. Calculate the spot rate's average logarithmic return and variance.b. What is the rate's annualized mean and variance?c. Calculate the spot rate's up and down parameters for
Given the following:- Current spot $=0.08$- Annualized mean for the spot rate's logarithmic return of 0.022- Annualized variance for the spot rate's logarithmic return of 0.0054- Binomial interest
Comment on the arbitrage-free features of valuing a bond using a binomial interest rate tree generated by estimating $u$ and $d$ in terms of mean and variance.
Explain the methodology for estimating a binomial tree using the calibration model. Comment on the arbitrage-free features of this approach.
Given a variability of $\sigma=\sqrt{h V_{e}^{A}}=0.10$ and current one- and two-period spot rates of $S^{m}{ }_{1}=0.07$ and $S^{m}{ }_{2}=0.0804$ :a. Generate a one-period binomial interest
Using Bloomberg's OVME screen, determine the equilibrium price on a selected call and put options on a futures contract on a T-Note or T-bond. For information on how to find options from the SECF and
Create a portfolio of at least two options on the same futures you selected and evaluate the position in terms of the position's OPM value, delta, gamma, and theta. On the OVME screen, click the +
Using Bloomberg's OVME screen, determine the equilibrium price on a selected call and put option on a Eurodollar futures contract. For information on how to find options from the SECF and CTM screens
Guide:- To find futures indexes on SECF, click "Fixed Income" from the "Category" dropdown and then click "futr" tab or click "opts." Use OMON on the futures screen to find the futures options.-
Find descriptions, recent prices, and other information on a convertible bond. Use SECF, SRCH, or CSCH to search for convertible bonds. Upload the convertible's menu screen (convertible's Ticker ).
Given the following interest-rate swap:- Fixed-rate payer pays half of the YTM on a T-note of $3.0 \%$- Floating-rate payer pays the LIBOR - Notional principal is $\$ 10$ million - Effective
Using a table showing payments and receipts, prove that the following positions are equivalent:a. Floating-rate loan plus fixed-rate payer's position is equivalent to a fixed-rate loan.b. Fixed-rate
Explain the alternative ways a swap holder could hedge her swap position instead of selling it to a swap bank.
If the fixed rate on a new par value two-year swap were at $3 \%$, how much would a swap dealer pay or charge to assume an existing fixed-payer's position on a $3.5 \% /$ LIBOR generic swap with
If the fixed rate on a new par value two-year swap were at $5 \%$, how much would a swap dealer pay or charge for assuming an existing 5.5\%/LIBOR floating-rate position on a generic swap with two
Given a generic five-year par value swap with a fixed rate of $6 \%$, determine the values of the following off-market swap positions using the YTM approach:a. Fixed-rate position on a five-year,
The Beta Chemical Company wants to finance an expansion of one of its production plants by borrowing $\$ 150$ million for five years. Based on its moderate credit ratings, Beta can borrow five-year
Suppose a company wants to borrow $\$ 100$ million for five years at a fixed-rate. Suppose the company can issue both a five-year, $6 \%$, fixed-rate bond paying coupons on a semiannual basis and
Suppose a financial institution wants to finance its three-year $\$ 100$ million floatingrate loans by selling three-year floating-rate notes. Suppose the institution can issue a three-year, \(7
Suppose a financial institution wants to invest $\$ 100$ million in a three-year fixed-rate note. Suppose the institution can invest in a three-year, $7 \%$, fixed-rate note payingcoupons on a
Suppose a financial institution wants to invest $\$ 100$ million in a three-year floatingrate note. Suppose the institution can invest in a three-year, $7 \%$, fixed-rate note paying coupons on a
Short-Answer Questionsa. Who generally assumes the credit risk in a brokered swap?b. Who assumes the credit risk in a dealer's swap?c. What is one of the problems with brokered swaps that contributed
Explain how a company planning to issue four-year, fixed-rate bonds in two years could use a forward swap to lock in the fix rate it will pay on the bonds. Explain how the hedge works at the
Suppose a speculative hedge fund anticipating higher rates in several years purchased a two-year payer swaption on a three-year 6\%/LIBOR generic swap with semiannual payments and a notional
Use the Bloomberg SWPM screen to create and analyze a fixed-/floating-rate swap. Tabs to include in your analysis: Main, Resets, Curve, Cashflow, and Scenario.
Use the Bloomberg SWPM screen to create and analyze a swaption on a fixed-/floating-rate swap similar to the one you created in Exercise 1. To create a swaption on SWPM, go to the "Products" tabs and
Construct a bond portfolio using PRTU or select a bond portfolio you have already constructed.a. On your MARS screen, create a fixed-payer position on a generic swap. Add your swap to a portfolio you
The Bloomberg ASW screen allows you to calculate the relative value of a selected bond through the interest rate swap market. Select a dollar-denominated, fixedincome, intermediate-term Treasury or
Given a discount rate of $5 \%$, determine the present value of the payments on a five-year CDS with a spread of $3 \%$ and a $N P$ of $\$ 100$. If the recovery rate on the underlying credit
Given an estimated five-year average probability intensity o f0.0375 on a five-year, BB-rated CDS, a recovery rate of $30 \%$, and discount rate of $5 \%$, determine the value and spread on the
The table below shows the historical cumulative probabilities for corporate bonds with quality ratings of B: Cumulative ProbabilitiesCumulative Probabilitiesa. Determine the conditional default
How much would a swap bank pay or require as compensation for assuming the buyer's position on a four-year BBB-rated CDS with a spread of 2.5\% if current four-year BBB-rated CDS are trading at a
How much would a swap bank pay or require as compensation for assuming the seller's position on a four-year BBB-rated CDS with a spread of $2.5 \%$ if current four-year BBB-rated CDS were trading
The table shows the annual loan rates that American and British multinational companies can each obtain on a five-year, $\$ 150$ million loan in dollars and an equivalent five-year, $£ 100$
Currency swap valuation questions:a. What is the bond equivalent of a currency swap position in which the counterparty agrees to swap a three-year, $10 \%$ loan of $\$ 15$ million for a
Explain with an example an operational exchange rate hedge or natural hedge. In your example, assume a US-owned company with its operation and sales in the United Kingdom, material expenditures in US

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