Questions tagged [options]

A contract that gives the owner the right, but not the obligation, to buy or sell a security at a fixed price in the future.

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2answers
45 views

Will the Delta of an Option always be the same irrespective of the underlying stock price?

Suppose, under the Black Scholes model we keep all the parameters the same except that we vary the asset price. Will the Delta of the option always remain the same?
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1answer
105 views

Simulating assets of different currencies

I have a situation as follows: One year call option on a Euro stock with a Euro denominated strike. Knock in feature as follows - The option can only pay out if the growth in the Euro stock over ...
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1answer
75 views

Trading Vol with options

One can trade vol swap to get exposure of the volatility of the underlying security in a 'clean' way. On the other hand, we know that vol swap, theoretically can be replicated by a dynamic position of ...
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0answers
27 views

FX Options Greeks: Is there a meaning in converting the sensitivities values in different currencies?

Suppose you have a Call on JPY, domestic currency is USD The price will be in USD Let's say delta = 0.93 Does it make sense for any reporting reasons to convert this value into JPY ? What is even the ...
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1answer
54 views

Black Scholes Replication If Underlying Does Not Move?

Let's say you are long a call and want to replicate that call buy being short underlying and long bonds. If the underlying moves up in the next period but not enough to cover theta, the option ...
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5answers
66k views

How can the implied volatility be calculated?

We all know if you back out of the B.S. option pricing model you can solve for what the option is "implying" about the underlyings volatility. Is there a simple, closed form, formula deriving Implied ...
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0answers
30 views

Implied volatility of Treasury options

For practitioners, does the concept of implied volatility also apply to (European) Treasury Options (whose underlying is Treasury Futures contracts)? For the standard individual stock vanilla ...
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0answers
54 views

Prove the following Call and Put relationship: [duplicate]

I need to prove that $$c(S,X,T)=\frac{X}{F}p(S,\frac{F^2}{X},T)$$ where $$F=Se^{(r-q)(T-t)}$$ I am having trouble proving this relationship. Is this relationship even possible? If so, can someone ...
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1answer
107 views

Any good book recommendations for learning The Greeks?

I am interested in getting a good "feel" or intuition for the BSM Greeks. Specifically, i'm looking for a book which is light on the math (but not too light) and easy to read and understand. I am also ...
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0answers
62 views

What is the cause of a “broken” volatility surface?

I am currently working on a project for which I need the implied volatility surfaces, to estimate the value of plain-vanilla European options with different strikes (cannot be observed directly in the ...
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1answer
36 views

In search of double barrier out option on a BM

We have a BM $X_t$ with $dX_t=\sigma dB_t$ ($X_0$ not necessarily zero!) under the risk neutral measure $\Bbb Q$. Given upper barrier $U$, lower barrier $L$, "strike" $K$ such that $L<X_0<U, L&...
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Why do simulation schemes have difficulty in pricing options with low spots?

If you apply a simulation Scheme (log-Euler discretization, Euler discretization and even more advanced ones) on for instance SABR and other models, then they price a call option (where we can easy ...
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49 views

Most efficient way to find Option IV using binomial/BS model

I have a python script set up to run a loop to plug in different values for IV into the binomial model to get an option price as close as possible to the market price. My issue is that at the moment ...
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1answer
77 views

Barrier option on a basket with arbitrary stochastic process

Suppose I want to price a Down-and-out European call, barrier option. However, the stochastic process is not a gBm or any other Levy process with known structure. Practically, I want a barrier option ...
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0answers
41 views

cashflow for floorlet option on 1 month Libor under Vasicek

I have to figure out the cashflow for a floorlet option written on 1 month Libor under Vasicek model by considering yield curve power series expression and bond pricing equation: Has anyone an idea ...
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0answers
38 views

Credit spread model

Let $c(t,T):=-\frac{1}{T-t}[\mathrm{ln}(P_1(t,T))-\mathrm{ln}(P_0(t,T))]$, with: $c$ measure of how a company is prone to fail; $P_0(t,T):=e^{-r(T-t)}$ price of no-defaultable bond. $P_1(t,T):=\...
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40 views

Put-call parity for equity share and debt share

Considering Merton's structural approach" for credit risk modeling, we arrive to prove that the pricing formules are $S_t=V_t\phi(d_{T,1})-Fe^{-r(T-t)}\phi(d_{T,2})$ for equity share and $F_t=FP_0(t,T)...
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1answer
284 views

When interest rates go up, why do call option prices go up?

I studied that generally speaking, interest rates and share prices have an inverse relationship. When interest rates go up, share prices go down. If interest rates go up, wouldn't people be less ...
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2answers
132 views

Forward Volatility vs Spot Volatility in Option Skew Models

My question is regarding Volatility Skew Models and their inputs. I have noticed that a vast majority of models take as an input the forward of the underlying (even in the case of stocks - where the ...
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3answers
223 views

Options Delta Meaning of Term [closed]

not able to understand delta in options. Whilst I understand, it is how much the option moves when the underlying moves by 1 unit, I fail to understand, when someone books a currency option, why does ...
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1answer
59 views

Super-replicating and sub-replicating portfolios and hedging

For recall, assuming that European options are traded at discrete strikes: the portfolio of vanilla options that minimally super-replicates an option $O$ is the portfolio of options that costs least ...
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0answers
41 views

Books and techniques to hedge options that expire tomorrow?

Can anyone point me to books or resources that talk about best techniques to hedge ATM or close to ATM options that expire tomorrow. I am particularly interested on how to hedge if you are short the ...
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3answers
3k views

What really is Gamma scalping?

How does Gamma scalping really work? It seems there is no true profit scalped. If we look at the simplest scenario, Black-Scholes option price $V(t,S)$ at time $t$ and the underlying stock price at $S$...
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1answer
82 views

Problem at deriving Bachelier formula with interest rates

In the Bachelier model, I have difficulties with a certain step. I want to figure out the distribution of $S_T$, which is the price process in the Bachelier model. So far I could state that ($\mathbb{...
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1answer
81 views

Equivalence of Put Pricing Formulas

I have to show that: \begin{equation} P_{t,T}(K)=e^{-r(T-t)} \int_0^{\infty}\left(K-S\right)^+ q_T^S(S)dS \end{equation} is equivalent to: \begin{equation} P_{t,T}(K)=e^{-r(T-t)}\int_{-\infty}^{...
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0answers
50 views

Measuring implied move priced into an event

It's well known that options price in an expected move in the underlying going into events, such as earnings announcements. I currently measure this implied move by computing the forward variance ...
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1answer
53 views

Computing option price with rates only

Hi I am learning about options and came across this example: The spot FX rate AUD/USD is 0.6868, the 6 month ATM implied volatility for AUD/USD is 7.7% p.a., for the 6 month USD deposit rate is 2.28% ...
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19 views

Pricing barrier option under Levy process: Biased estimate?

I want to price a down and out call, barrier option, with the underlying asset following a Levy process. I am interest on the Kou double exponential model or the NIG process, to capture asymmetric ...
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30 views

Is the implied volatility surface relative or stationary?

Do different strike values of options attain their volatility value dependent on their % distance from the ATM price continuously, or is the volatility surface stationary during a single day?
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1answer
82 views

Black's Approximation - Discrete dividend for Put Options

I am currently trying to price and option chain for dividend paying stocks (american style exercise). I am able to calculate the Net Present Value (NPV) of dividends until maturity and then apply ...
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0answers
40 views

Why can't we create a “magic” basket of options to sell for no-arbitrage pricing in SVJ model?

I am learning how to price SVJ options and am reading some stuff on no-arbitrage pricing for SVJ model using the typical approach you would use (like in BSM option pricing) of creating a risk free ...
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1answer
83 views

How to interpret the (expected) exposure and CVA of an option or a single share

I have a quick (hopefully simple) question regarding the interpretation of the expected exposure of a call option and a single share. I've done some computations on the formula for the expected ...
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One-day Binary Event Implied Moves

What is the convention for pricing the expected 1-day move of a binary event based off of the implied volatility of the nearest series which contains that event? How do you distinguish between the ...
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1answer
76 views

Pricing structured products (Mortgage Backed Securities) [closed]

What would someone have to do to be able to price a structured product like Mortgage/Asset Backed Securities?
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65 views

Option Prices on Thomson Reuters Eikon Database

I would like to get hist. option prices from Eikon. I am not looking for the entire option chain and I was wondering if Eikon offers average data/prices. Average European call and put option prices ...
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70 views

Practical Skew Model For Equity Options?

I'm looking for a simple model I can use to calibrate equity implied volatility surface. There are several models published in the literature, and most of them seem far too sophisticated for my ...
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1answer
65 views

American Put Option Pricing

I am trying to solve a question of American Put Option pricing as below. Build a 15-period binomial model whose parameters should be calibrated to a Black-Scholes geometric Brownian motion model with:...
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1answer
121 views

What is the easiest way to learn Option pricing with PDE?

I was reading about Ito's formula and Girsanov theorem, but I am still struggling to grasp how in reality these are combined to compute the price of an option. What are the main source to understand ...
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0answers
53 views

How would one go about pricing a FX future?

What model/equations would I require to calculate the price for a foreign exchange future? This is in an attempt to mitigate foreign exchange risk. Also, how could one measure a business's exposure to ...
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1answer
36 views

Is the undiscounted value process of a Euro call option under Bachelier model a Martingale? [duplicate]

Assume that $c_t$ is the UNDISCOUNTED price process for a European call option in Bachelier model. In Bachelier model call option pricing formula the formulas is discussed. The undiscounted value ...
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1answer
103 views

Least Squares Monte Carlo

Could you explain to me in words (no formulas) the concept of the Least Squares Monte Carlo method to price an American style option?
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0answers
67 views

Valuation of Callable Bonds

Is there any way to price American Callable Bonds (those which can be called on any date before expiration) other than basic CRR interest rate trees, since they won't be accurate enough to give ...
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1answer
3k views

Gamma Imbalance Explanation

Can someone please give me an explanation as to what put-call gamma imbalance specifically refers to (imbalance of what?), and why they may exacerbate volatility from a market perspective, and why the ...
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2answers
2k views

How is the Chooser Option's value computed in this example?

In preparation for my finals, I am attempting a question on chooser options. One question asks A European chooser option on an index ETF paying a yield of 3.0% with strike \$64 has a maturity of ...
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1answer
47 views

How underlying asset price variance is connected with time

I'm dealing with option pricing models and there is a statement that says the variance of underlying asset price is propotional with time $𝑉𝑎𝑟(𝑆_{𝑚+1})=𝑆_𝑚^2𝜎^2Δ𝑡$ where $\Delta t = \frac{T}{...
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1answer
248 views

Options Pricing and Mean Reversion

I'm confused about the impact that a mean reverting stock price process has on the value of an option on it. Several sources say that there is indeed an impact on the price of an option: Option ...
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0answers
122 views

Calculating dealer gamma imbalance/exposure for an options strip

Have seen this being done for years (primarily by J.P. Morgan and a couple other bank research desks) and am attempting to re-create for my own personal research. I’ve read the forums on here but no ...
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1answer
27 views

Historical quotes / prices of multiasset options

I am working on Lévy copulas, and I would like to try calibrating such techniques on real data. Where can I find quotes for multi-asset options? It could be exchange options or any other type of ...
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0answers
69 views

What exactly does shifting a barrier in a barrier option mean and how does it hedge delta?

How exactly is shifting the barrier to hedge delta implemented in case of barrier options. Is it just changing the barrier, if so, how does it hedge delta or is it making the barrier a range like a ...
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How can I graph futures options profit/loss when the options have different underlyings?

Consider a portfolio of vanilla SPX monthly options that consists of two components, a SEP 2019 3000 Call and a DEC 2019 3000 Call. It's easy to graph these as they both share the same independent ...