Questions tagged [derivatives]
A financial contract whose payoff is linked to the evolution of an underlying security.
359
questions
0
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1answer
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,...
-1
votes
0answers
31 views
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 ...
1
vote
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 ...
2
votes
1answer
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 ...
0
votes
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 ...
2
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0answers
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 ...
2
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0answers
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 ...
0
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0answers
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?
2
votes
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 ...
1
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0answers
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 ...
0
votes
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)...
0
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0answers
35 views
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 ...
1
vote
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 ...
2
votes
0answers
22 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 ...
2
votes
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 ...
0
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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 ...
0
votes
1answer
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 ...
1
vote
2answers
144 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 ...
3
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5answers
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) ...
0
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0answers
18 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 ...
0
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0answers
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 ...
0
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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, ...
1
vote
0answers
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:
$$
(c + j \omega) F(\omega, 0) = e^{-rT} e^{-a(c+j\omega)}...
0
votes
1answer
70 views
What to do if certain parameters are not market observable?
Lets say I have no clue on correlation between 2 equities in the market (i.e. i don't have an observable market price). What is the best way to go about marking this correlation for lets say the best ...
0
votes
1answer
46 views
Equal prices for call and put options with symmetric strikes around contemporaneous price?
Shouldn't (according to the Black-Scholes model) the price of a call option with a strike of an arbitrary amount away from the current asset's price, be equal to the price of a put option with the ...
2
votes
1answer
78 views
Callable Total Return Swap pricing
I need to price a callable Equity Return Swap by Accrual. ERS has property callable T+1 and I don't get it. Does it mean that when a call happen we fix a price that and pay Accrual the next day? Could ...
1
vote
0answers
14 views
Balance sheet items which might show exposure to hedging or the prevalence of forward contracts
I do have a panel data set on North American companies from Compustat covering balance sheet and income information. I am wondering if there is a possibility to use a balance sheet variable as an ...
0
votes
1answer
87 views
Calculate Third Order Greeks Options
Hope you're doing great! I'm struggling to develop the code for the Third Order Greeks.
In all places I have searched, the development is missing.
For example:
But I don't know how to develop it, ...
5
votes
2answers
111 views
Radon Nikodym derivative when changing numeraires
I note from Wikipedia that if $Q$ and $Q^N$ are two measures corresponding to numeraires $M$ and $N$, then the Radon Nikodym derivative is given by: $$\frac{dQ^N}{dQ} = \frac{M(0)}{M(T)}\frac{N(T)}{N(...
0
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0answers
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, ...
0
votes
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 ...
1
vote
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)...
0
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0answers
20 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 ...
4
votes
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 ...
1
vote
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 ...
0
votes
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 ...
1
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0answers
43 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 ...
1
vote
3answers
96 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?
1
vote
1answer
44 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/...
0
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0answers
57 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 ...
0
votes
1answer
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 '...
0
votes
0answers
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 ...
1
vote
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}.
$...
0
votes
0answers
33 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 ...
0
votes
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 < ...
0
votes
2answers
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,...
1
vote
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 ...
1
vote
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 (...
1
vote
0answers
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 ...
0
votes
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 ...
