Questions tagged [derivatives]

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

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4answers
15k views

What is a Constant Maturity Swap (CMS) rate?

I have been searching in books and on the internet for a basic definition and explanation of CMS rates, but I cannot find anything clear and simple. Can you explain (maybe with an example) what a CMS ...
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1answer
44 views

Is the forward price equal to the future price?

If $f^{T_1}(t)$ is the price of a forward and $F^{T_1}(t)$ is the price of a future on some stock, both maturing at date $T_1$ and with the assumptions: no dividend constant interest rates no ...
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31 views

dB=rBdt: express B(T) in terms of B(t) [closed]

Consider a risk free asset with continuously compounded return of r. Let $B$ be value invested in the asset. $dB=rBdt$: write the expression for $B(T)$ in terms of $B(t)$
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1answer
69 views

What to do if certain parameters are not market observable?

Lets say I have no clue on correlation between 2 equities in the market (i.e. i don't have an observable market price). What is the best way to go about marking this correlation for lets say the best ...
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0answers
17 views

Local v/s global calibration for a Bermudan Option (calibrate co-terminals vs entire matrix)

I am quite new to rates modeling and I have a question on the pros and cons of calibrating to larger set of vanilla instruments v/s calibrating to an exotic's 'natural' hedges. For example, I could ...
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5answers
467 views

bank issuing structured products

"The investment banks supplying structured products were effectively buying options from investors" How to understand this quote from this source? I would think the investors are usually had (long) ...
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1answer
109 views

Do different prices under different models admit arbitrage?

There are many models for interest rate. If two people use two different models to price the same interest rate derivative, and come to two different prices, doesn't that admit an arbitrage? How ...
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1answer
60 views

Extensive list of financial derivatives and what method is used to value them

What I'm imagining is a long list of different types of financial instruments traded on the market along with the model(s) that is industry standard for valuing it. Something like: European equity ...
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0answers
44 views

Issue with solving American call option questions

Here are the questions: I tried using DerivaGem, but I am not sure that I got the right result. Here are my attempts at solving the questions: a) Upper and lower bound: Is it correct? Not sure ...
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2answers
125 views

What does the word “affine” mean in affine term structure models?

I am new to the field of Mathematical Finance and wanted to get an idea on the intuitive, physical and mathematical meaning of the term "affine" in Affine term structure models. Any literature ...
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1answer
306 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}-...
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1answer
87 views

Understanding the notion of future options

I am currently studying different types of option-related derivatives and I am quite confused about the notion of “futures options”. My textbook says that A futures option is the right, but not ...
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1answer
52 views

Is there a reason why futures and options have more substitutes than other financial instruments?

This is somewhat non-technical question, but it seems like this forum is still the best place for it. I'm reading Shleifer's Inefficient Markets, where he points out that [...] for futures and ...
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1answer
74 views

Callable Total Return Swap pricing

I need to price a callable Equity Return Swap by Accrual. ERS has property callable T+1 and I don't get it. Does it mean that when a call happen we fix a price that and pay Accrual the next day? Could ...
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3answers
217 views

How do market makers chose the size that they quote?

A typical quote in the derivatives market may be 2.00 bid at 2.50 ask with a size of say 100x100. How do practitioners go about choosing the size of the market (how many contracts) to quote? It seems ...
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15 views

Contingent Claim Bounds

In my course on discrete-time finance we derived the following equality for a lower bound for the value of a not necessarily replicable contingent claim $D$. Here we are looking at a single period ...
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0answers
60 views

Types of financial derivatives

I am looking for an explanation for different types/grades of derivatives. For example we have various asset classes: equities FX (currency) derivatives, etc. Or different types of secured debts, ...
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0answers
33 views

Is Vega hedging a complex derivative self financing?

Let's consider an incomplete market where I am pricing a complex derivative (Say a Bermudan). I hedge vega by a vanilla option(S). Let's say at t=1 I want to re-hedge. However, I have no guarantee ...
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2answers
105 views

Radon Nikodym derivative when changing numeraires

I note from Wikipedia that if $Q$ and $Q^N$ are two measures corresponding to numeraires $M$ and $N$, then the Radon Nikodym derivative is given by: $$\frac{dQ^N}{dQ} = \frac{M(0)}{M(T)}\frac{N(T)}{N(...
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30 views

Fourier transform of price function

If the expiry value is given by $f(x,T) = e^{-c x}$ for $x \ge a$ and 0 otherwise and c is a +ve constant, prove that in the Fourier domain: $$ (c + j \omega) F(\omega, 0) = e^{-rT} e^{-a(c+j\omega)}...
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1answer
999 views

Stochastic modelling of derivatives on dividends

I consider pricing and risk analysis of derivatives on dividends of the members of equity indices (such as Dow Jones EuroStoxx). There are options but I focus on futures. What are common stochastic ...
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1answer
42 views

Equal prices for call and put options with symmetric strikes around contemporaneous price?

Shouldn't (according to the Black-Scholes model) the price of a call option with a strike of an arbitrary amount away from the current asset's price, be equal to the price of a put option with the ...
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1answer
84 views

Calculate Third Order Greeks Options

Hope you're doing great! I'm struggling to develop the code for the Third Order Greeks. In all places I have searched, the development is missing. For example: But I don't know how to develop it, ...
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0answers
13 views

Balance sheet items which might show exposure to hedging or the prevalence of forward contracts

I do have a panel data set on North American companies from Compustat covering balance sheet and income information. I am wondering if there is a possibility to use a balance sheet variable as an ...
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29 views

Models for derivative portfolio composition

I focus on interest rate derivatives. I am looking for theoretical references which would model how financial institutions optimally choose among the different types of existing instruments (options, ...
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1answer
32 views

Synthetic FRAs using Eurodollar futures

In order to create a synthetic FRA position of 30-day FRA on 90-day LIBOR, the diagram below shows that we can enter into positions by going long a 120-day Eurodollar contract and short a 30-day ...
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1answer
32 views

The NA price of a caplet with payoff

Prove the following statement: The NA price of a caplet with payoff $$\delta \cdot (L(T;T,T+\delta)-k)^{+} $$ at time $T+\delta$ equals the NA price of a put option with the payoff $$(1+\delta \cdot k)...
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2answers
214 views

When would open interest equal trading volume?

I know the difference between open interest and trading volume. Open interest is the number of contracts, long or short, outstanding. Trading volume is the number of contracts traded in a day. ...
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0answers
19 views

Bond CSA hedging risk

If I have a CSA that contains say GBP Gilts and GBP cash, how do i hedge the risk that the gilt funding cost goes up. Lets say my portfolio is > 10 years. Let's assume I have a discount curve that ...
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2answers
180 views

Why do some principal-protected notes reset the gains to zero?

I was looking through the principal-protected notes issued by Lehman Brothers. One of them was the "100% Principal Protection Absolute Return Barrier Notes Linked to the S&P 500 Index". The ...
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0answers
67 views

Trading options - real life vs. textbook?

I'm a Management with Finance student and we have recently learned about options. Because I find it easier to learn these things when I have some context to apply them to, I put $100 in my brokerage ...
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0answers
42 views

Application Itô's Lemma: Forward to Spot process

I am working on the following equation (I want to apply Ito's lemma on it): and I know that: and also and My problem is that I want the dynamic of F(S,T) without S because I need first to ...
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3answers
94 views

Does a future contract's price show where investors think the underlying asset's price would be?

When the price of an asset's future contract is at a certain level, does that mean investors as a whole expect the actual underlying asset to reach that price level in the future?
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1answer
42 views

Different performance between GLD, IAU and PHYS

At this very moment (about 10:15, 2020/3/24), GLD/IAU are up about 4.5% and PHYS about 3.5% What causes such differences? Gold bars are in short supply around the world (https://www.ft.com/content/...
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56 views

How does modeling provide an edge to banks in the derivatives space?

I was thinking about the actual need for creating quantitative financial models, especially for derivative products. Consider simple calls and puts for different strikes and expiries on stocks and ...
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1answer
188 views

Python Quantlib : How to value the Non Deliverable currency Interest Rate Swaps?

I followed all the procedure in Quantlib to process interest rate swap valuation through Python Quantlib. I valued more than a million records. All the valuation is almost the expected amount. But '...
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0answers
89 views

Duration of forward starting swap

For a spot starting interest rate swap, the duration is calculated as the duration of the fixed rate leg less the duration of the floating leg. Each of these calculations is akin to calculating the ...
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1answer
162 views

Going from $\mathcal{P}$ to $\mathcal{Q}$

Under $\mathcal{P}$, we have the Heston Model given by: $$ d S_{t}=\mu S_{t} d t+\sqrt{\nu_{t}} S_{t} d W_{t}^{S},\\ d \nu_{t}=\kappa\left(\theta-\nu_{t}\right) d t+\xi \sqrt{\nu_{t}} d W_{t}^{\nu}. $...
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1answer
161 views

What happens to both sides of an inflation swap agreement if there is deflation?

If there is deflation does the Inflation receiver not only pay the fixed leg but also receives a reduced CPI? I.e. does he lose twice?
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2answers
172 views

Hull-White Calibration /Hypothetical Cap Pricing

I have a question regarding calibrating Hull-White (Extended Vasicek) Model to bond data. As you know, and stated in Mercurio (2005), zero coupon bond price in the Hull and White (1994); $P(t,T)=A(t,...
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0answers
32 views

Calculating the total return on an Interest Rate Swap (with 1 year of duration)

Say I am the fixed rate payer on an interest rate swap and have 1 year of duration of exposure. When I entered into the IRS (say yesterday), the quoted rate on Bloomberg was 15%. Say tomorrow the ...
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3answers
249 views

How do derivatives affect capital structures?

Yesterday, I was at a lecture where the speaker said that the impact of derivatives was often to make senior debt, in effect, subordinated debt (in terms of priority, recovery rates, etc.)? How do ...
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2answers
68 views

Option on a dice game with three dices and min. value

We have a call option on 3 dices with strike 3. What's the fair value of the call when it pays the min value of the 3 dices? E.g if we throw and have 426, the min is 2 here and so call is OTM (S < ...
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1answer
76 views

Arbitrage when discounting and forward computation is done with different curves

I notice that (equity derivatives) trades generally are priced with different forward curve and discounting curve, which clearly lead to arbitrage. Is this arbitrage value too small to be ignored? How ...
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1answer
118 views

Intuition for consistent Derivative Prices under different Numeraires and Measures

This is essentially the Fundamental Theorem, however I am not asking for a thorough proof, I am more interested in the general intuition. In words, it makes sense that whatever your unit of account (...
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0answers
63 views

Calculate upper bound for put option prices?

I need to know historical option prices for backtesting. The problem is I don't have such historical data. Is there a way to calculate the upper bound for out of money (American) put option selling ...
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1answer
47 views

What is the difference between exercise and expiry date?

I know in American options you can exercise the options at any time before expiry date but in European options you can only exercise the options on expiry day. On National Stock Exchange of India the ...
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1answer
183 views

Cap price as bond options

I am currently struggling with model calibration of the Hull-White (or Vasicek) model to Caps and Floors. My main problem is that I am confused about the notation. In Brigo & Mercurio (2006, p. ...
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0answers
35 views

Derivatives - how to build the term structure of the cost of carry

1) By using the settlement prices, build the term structure of the cost of carry for the contract. Use the first two contracts to extract the implicit index that you will be using for all the ...
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1answer
51 views

partial derivatives of multivariable function

Looking to verify whether the following formulation is correct. Suppose we have the following function, relationships: $$y=f(x)$$ $$x=g(a,b)$$ $$y=f[g(a,b)]$$ Is the below correct (including ...

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