Questions tagged [derivatives]

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

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74 views

Computing $\mathbb{P}(S_T > K)$ under the stock measure

Develop a formula for the price of a derivative paying $$\max(S_T(S_T-K))$$ in the Black Scholes model. Apparently the trick to this question is to compute the expectation under the stock measure. So,...
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Where to begin? [duplicate]

I have a strong background in Maths & Stats, undergrad + masters from a top uni. Been working as a Data Scientist the past year and learnt a lot of programming (Python/R/SQL/KDB/Java) and Machine ...
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1answer
170 views

Software implementation for valuation of exotic options

I am looking for some software implementation of pricing Average Price Call option (APO) mostly Python (or any other package.) Exercise style is ...
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97 views

What kind of entities use exotic derivatives, and do they serve any purpose other than hedging risk?

I work in a sell-side bank in derivatives modeling. My work involves modeling and pricing of exotic derivatives and I often wonder who are the buyers of these products. From my research, I found that ...
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1answer
49 views

Convexity of a rates Bermudan w.r.t strike

Recently there was a nice question asked on convexity of American put w.r.t strike: Convexity of an American put option Does the same hold for a Bermudan option in rates, where they underlyings are ...
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25 views

Does equity premium puzzle affect option-implied RWDs using Arrow-Debreu equilibrium?

I am researching and learning about option-implied RNDs (risk neutral densities) and transformation to RWDs (risk world densities) using expected utility theory to compute risk aversion values. This ...
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49 views

What are the most difficult/computationally expensive/infeasible derivatives to price?

I'm not sure if this question has a concrete answer or if it's more of a fun game, but I suppose the question that does have a concrete answer is what's the most difficult instrument to value that has ...
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28 views

Black model with negative strike price

Whats the issue if we try to price a swaption with a negative strike using Black model?
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1answer
70 views

Bermudan option exercise probability when rates rise

I am looking for an explanation of what happens to the Bermudan exercise probability (i.e. does probability of early exercise go higher if rates rise or lower) w.r.t rates. This is of course with ...
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47 views

Options pricing model inversion

He cited about Roll's compound formula for finding the lead-lag effects between stocks and options. I have a similar data for National Stock Exchange's Index, NIFTY but it's daily, not intra-day. I ...
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2answers
77 views

lead lag relationship among futures, options and stock prices

I have the data of past 10 years of NIFTY (the National Stock Exchange of India) stock, futures and options and I want to show the lead-lag relationship (which reacts first, futures, options or stocks)...
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How do I calculate FX forward hedge ratio?

Suppose I have a USD holding of 1,000,000 in my portfolio and I want to convert it into EUR in a month's time. I enter into a FX forward contract of the same amount USD 1,000,000, meaning that I have ...
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1answer
47 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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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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1answer
114 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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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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63 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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2answers
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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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489 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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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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36 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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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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31 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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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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1answer
46 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
78 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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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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87 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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111 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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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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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
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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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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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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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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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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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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
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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
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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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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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225 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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112 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
164 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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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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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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184 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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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
128 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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65 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
50 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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