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Questions tagged [derivatives]

A financial contract whose payoff is linked to the evolution of an underlying security.

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Non deliverable interest rate swaps (NIRS)

Can you pls explain how the payoff of an NIRS is calculated and what collateral is usually posted (USD or local ccy)? I am especially interested on how the FX risk is incorporated in the pay off and ...
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Simple arbitrage pricing of bond option

This is Tuckman fixed income security textbook. The text here is trying to price a 990 six month call on a six month zero bond. When we replicate the portfolio, where is the F_.5 coming from? My ...
1 vote
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Implicit function theorem and sensitivities to market risk for Nelson-Siegel-Svensson model

I’m calibrating the Nelson-Siegel-Svensson model to market rates and I’m trying to compute the sensitivities of the NSS parameters to those said rates: $$r\left(T\right)=\beta_{0}+\beta_{1}{\frac{\...
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32 views

Resources to understand derivative pricing and simulation models and aggregation of risk measures

I am looking for a book or set of videos which explains theorems and models of quantitative finance and stochastic calculus required for understanding derivative pricing and simulation in a very ...
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1 answer
215 views

Monte Carlo methods: Choosing the best measure

When pricing derivatives using Monte Carlo methods, we take outset in the risk neutral pricing formula which states that we need to calculate the expected value of the discounted cashflows. To do this,...
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1 answer
67 views

An application of Ito's formula with correlated Brownian increments

I am beginning to study (applied) stochastic calculus. I'm unclear on the following calculation which I am attempting to perform. I am attempting to show that if we have $$\begin{cases} dS_1 = a_1(S_1,...
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1 answer
73 views

Best Book - Understanding Investment Bank Operations

Could you please recommend Books to read for understanding Investment bank operations in Information Technology ( IT ) Point of view? like develop/support all system involved in FO/MO/BO systems in ...
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70 views

Find a formula for the price of a derivative paying $\max(S_T^2-K,0)$ [duplicate]

Develop a formula for the price of a derivative paying $$\max(S_T^2-K,0)$$ in the Black Scholes model. What I tried: \begin{align*} e^{-rT}\mathbb{E}^\mathbb{Q^0}[\max\{S_T^2-KS_T,0\}] = e^{-rT}\left(...
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1 answer
168 views

Derivatives: Value vs Notional/Principal amount

I am reading "Options, Futures and other Derivatives" by John Hull. In chapter 1, a section on OTC market size has the following lines. Figure 1.1 compares (a) the estimated total principal ...
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1 answer
79 views

Notional Value of Worldwide ETD vs OTC Open Interest

I request assistance to find the Notional Value of Worldwide Open Interest of Exchange Traded Derivatives (ETD). As per this FIA link, the total open interest at the end of April 2024 was 1.33 billion ...
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1 answer
96 views

Where can I find implied rates for central bank decisions?

Sometimes I'll see sources online say things like markets are pricing in a certain amount of bps rate cuts/hikes by the Fed or ECB (or some other central bank) for a certain monetary policy meeting ...
2 votes
1 answer
195 views

Brazil IR swaps and help with new holiday

Brazil has a pending new holiday that is expected to be official in the next month, for date Nov 20. Existing BRL interest rate swaps contracts have a clause that fixed accruals are not impacted by ...
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1 answer
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variation margin affecting futures price

A quote from Natenberg's Option Pricing and Volatility, on stock index futures and how variation margin can change their price. Ignoring dividends, the fair value of a stock index forward contract is ...
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Why do we use OTM options to extract implied vol?

It is often common practice to calculate implied volatility using puts for low strikes and calls for high strikes, so to always employ out-of-the-money options. Why is this often preferred to using ...
2 votes
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What are common parametric forms for VIX smiles?

It is common in SPX markets to fit smiles using Stochastic volatility-inspired and Surface stochastic volatility-inspired parametric forms introduced by Gatheral and Jacquier (2014). In VIX markets ...
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2 answers
115 views

time value of option proportional to sqrt(time)

I'm reading Natenberg's Options Pricing and Volatility, and in Chapter 18, he mentions this about an example: We can further refine our approximation if we note that an at-the-money option is made up ...
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Pricing a custom option in terms of simpler instruments

I have the following custom European Option $F$ on the underlying $S$ whose pay-off at expiry $T$ follows: $$ F(T) = \min{[B, \max{[K_1-S(T), S(T)-K_2,0]}]} $$ where $B$ is a cash position and $0<...
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Callable Bond Delta Profile

I am analyzing a callable bond with 10 Years of maturity coupon paid monthly at market rate plus the spread of 25 bps. The bond has an American Call option embedded. The strike price of a bond option ...
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2 answers
3k views

What is CVA (credit valuation adjustment)?

According to Wikipedia, CVA is defined as the difference between the risk-free portfolio value and the true portfolio value that takes into account the possibility of a counterparty’s default. What ...
2 votes
1 answer
592 views

Exercise Probabilities Vanilla Cap/Floor

When looking at the discounted pay-off formulas of a vanilla caplet and a vanilla floorlet $\frac{\Delta\tau}{1+r_k\Delta\tau}\max(r_k-r_{cap},0)$ $\frac{\Delta\tau}{1+r_k\Delta\tau}\max(r_{floor}-...
3 votes
2 answers
310 views

Bid Price of a Forward?

Say I am a market maker. The ask (me selling it) formula is pretty common in textbooks etc by no arbitrage: $$F = S \cdot \text{exp}(r-d)$$ where $r$ is interest rate and $d$ -- dividend. Again, by no ...
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1 answer
127 views

Question on unwinding cross-currency swap

Hoping someone can help me understand 'Notional Exchange Unwind Value - NEUV' when terminating a cross currency swap prematurely. Where the NEUV is essentially the profit/loss of the notional exchange ...
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1 answer
136 views

Pricing look-back option

I have the monthly price data of a stock starting from December 2020 and I am considering a EU style look-back option issued in December 2020. The payoff at maturity of the look-back option is given ...
4 votes
2 answers
333 views

Does value of a TRS only involve past price movement and not expected returns?

Is the value of a TRS just the difference between the "financing leg" (e.g. the side paying -IBOR plus spread) and "asset leg" (e.g. the side pay income and price changes), with of ...
3 votes
1 answer
95 views

Benth: Risk-neutral measure in incomplete markets

I am currently working on Benth and Benth "THE VOLATILITY OF TEMPERATURE AND PRICING OF WEATHER DERIVATIVES" and i am stuck at following paragraph at page 10, which is about risk-neutral ...
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1 answer
113 views

Quantlib Vanilla Swap Amount not based on Forwards

I have the following code: ...
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53 views

Hedge Effectiveness

I am trying to prove the hedge effectiveness of a SWAP, I know that a regression needs to be done between the hedged item (Loan) and the hedging instrument (SWAP), but I don't know which values should ...
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44 views

Price Path Dependent Swap

Let's say we start at t0, with a vanilla XCCY Swap contract (one leg paying Fixed Rate r, and denominated on Ccy1, the other leg paying Floating Rate f on Ccy2). Now let's assume you have two ...
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1 answer
128 views

Calibrating SABR -- Can I calibrate the forward like any other parameter?

Essentially the title to the above. I am using SABR to price caps and floors (as well as options on SOFR futures). I currently have two calibration techniques, the first calibrates based on rho and nu ...
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1 answer
442 views

Carry for an Interest Rate Swap

I don't get why for calculating the carry of a spot starting swap I need to adjust the difference between the fixed rate and fixing by the Dv01? For example if I receive in a 5y swap and want to ...
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1 answer
89 views

futures exposure targeting (spot vs futures price)

I'm confused over if I should use spot or futures price when targeting a certain exposure. There are many websites that state you should use the contract size * futures price. Other websites, however, ...
1 vote
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28 views

Decomposition of Step-up swaps

is there a general procedure to decompose a fixed-floating interest rate swap, where the fixed rate changes period-to-period, into a basket of co-initial swaps, each with a different fixed rate? For ...
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1 answer
109 views

Can someone please help me answer this question about Black-Scholes model? (risk-neutral & true probability of the call option) [closed]

I don't even know where to get started with this question...can someone please help me? How do I answer it?
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1 answer
141 views

How to Correctly Price Currency Forwards/Futures [duplicate]

I am trying to understand how to price a forward contract on the GBP/USD currency pair and then compare my answer with current future prices on GBP/USD. If my understanding is correct I believe we ...
4 votes
2 answers
3k views

Which models do Bloomberg/Reuters use to derive implied volatility for interest rate derivatives with negative forward rates?

can anybody tell me which models Bloomberg and Reuters ares using to derive implied volatility for interest derivatives with negative forward rates? I know that Black-76 is the standard model, and ...
1 vote
1 answer
249 views

What is the purpose of a floating interest rate leg on an autocallable equity swap transaction?

I understand that the purpose of the equity leg is to hedge the issuers exposure under the note but I don't understand why the buyer of an autocallable equity swap pays a fixed fee at the beginning of ...
1 vote
1 answer
90 views

WN 30Yr UST Futures Conversion Factor vs Delivery Ratio

What is the logic behind using the conversion factor in determining the hedge ratio of deliverable bonds in 30Yr UST futures (WN contracts) throughout the trading life of the contract, but then having ...
3 votes
1 answer
238 views

Computing Derivative Security with Change of Numeraire

Under Black-Scholes, price a contract worth $S_T^{2}log(S_T)$ at expiration. This is a question from Joshi's Quant Book (an extension question). Ok, so I solved this with 3 different methods to make ...
2 votes
1 answer
100 views

Why A Derivative With Intrinsic Arbitrage Cannot Be Valued & Hedged With Assets In Risk Neutral?

I'm attempting to concisely show why a derivative that, by nature, introduces arbitrage cannot be valued using risk neutral pricing tools. Derivative: Buyer is sold a 'call option', with time 0 value ...
1 vote
1 answer
271 views

Moneyness, implied volatility and option greeks

I know that the more an option is ITM, the more is the implied volatility. I would like to deep dive into the concept, what is the logic that drives this statement? Also comparing an option with a ...
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PFE "convergence"

I'm studying Counterparty Credit Risk. I was reading about Potential Future Exposure (PFE) and I've seen a lot of examples and graphs about how the PFE behaves (as the time horizon increases) for ...
5 votes
2 answers
225 views

VIX future's lower and upper bounds

A Tale of Two Indices, by Carr and Wu (Jrl. of Derivatives, Spring 2006) As per the above paper of Carr and Wu (page 24 and 25), the price of a VIX future has for lower bound the fair strike of a ...
-1 votes
1 answer
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What book/resources would you recommend for beginners in IRD? [duplicate]

I recently graduated with a MS degree in Quantitative Finance and will presumably have some work to do with Interest Rate Derivatives (IRD) in the future. Since my experience lies more in the equity ...
2 votes
0 answers
113 views

Interest rate derivatives market data - download [closed]

EDIT; I looking for sources where from I could get interest rate derivatives market data? (caps,floors,swaptions, etc, is there data available for exotics ones or are they purely OTC?) I would grade ...
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2 answers
132 views

Constructing payoff with options

Suppose that COMPANY A has issued a special bond that does not pay any coupons. At maturity T, the bondholder receives the principal (face value) equal to 1,000 plus an additional ...
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1 answer
212 views

Calculating key dates for a Forward Starting Interest Rate Swap versus a Spot IRS

How are the Effective Dates and Maturity Dates of a forward starting IRS (eg: EURIBOR3M 5Y5Y) handled when the forward starting term ends on a non-business day? And if that date is adjusted, how does ...
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1 answer
171 views

Any other ways to hedge a bond portfolio against interest rate risk? [closed]

I'm currently taking a (gentle) intro to derivatives class. One of the exercises asked me to discuss duration as a risk measure and to provide alternative methods of hedging a bond portfolio against ...
0 votes
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191 views

How to convert the parameters of multi-factors cheyette model (quasi-Gaussian model) from tenors to factors?

The book "Interest Rate Modeling" by Andersen and Piterbarg is an extermely fascinating book on interest rate derivatives. Recently, I have encoutered some issues while reading this book. ...
5 votes
3 answers
536 views

How does the underlying get delivered for electricity market derivatives?

I have been reading around energy markets recently and recent schemes such as Voluntary Carbon Markets, similar to the 'cap and trade' style of the Kyoto Agreement in 1997. I have been reading in ...
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Barrier Reverse Convertible on interest rate

I'm trying to find the price of an barrier reverse convertible on interest rate - https://structuredproducts-ch.leonteq.com/isin/CH1251797945. I have simulated the underlying interest rate by Vasicek ...

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