Questions tagged [put-call-parity]

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1answer
119 views

Calculate forward price based on option chain

I've got historical data for a spy option chain which looks as follows ...
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1answer
59 views

Boundary for European Put Option

As an entry level financial engineer, I'm learning about call-put parity, which helps us to get the boundary for call option: $S-Ke^{-rT}\leq c\leq S$, what about put option? Should its upper bound be ...
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0answers
32 views

What is the effect of put call open Interest on price action

how option put call open Interest affects price actions as put sellers feel price when price goes down or call sellers feel pain when price goes up and how this affects price action. ie when price ...
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1answer
141 views

Proving the put call parity

In my course notes on the put-call parity, the proof is presented by going over two inequalities, namely $\text{RHS} > \text{LHS}$ implies arbtirage and $\text{RHS} < \text{LHS}$ implies ...
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2answers
82 views

Why are put and call options worth the same despite that put has no upside whereas call has unlimited upsides?

The following is an interview question. All Black-Scholes assumptions hold. Assume no dividends. Consider a standard European call and a standard European put on the same stock. Assume that each ...
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1answer
64 views

Time to Put or Call a Bond

I was studying putable bond and callable bond on my own, there is an exercise question that was a little confusing to me: I understand what the answer explains, but I am confused that, is a bond "...
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1answer
217 views

Continuous Geometric Asian Options

Assume the risk-free bond $B_t$ and the stock $S_t$ follow the dynamics of the Black & Scholes model without dividends (with interest rate r, stock drift $\mu$ and volatility $\sigma$). Let $c(t; ...
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1answer
57 views

How to prove Gamma is the same for a European call and European put with the same inputs?

I saw from a text "From put-call parity, call and put with the same inputs have the same gamma", but I don't see how put-call parity is related to Gamma. Can someone explain? Thanks!
2
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1answer
169 views

Why is put-call parity defined differently by CME and Wikipedia?

In general, Wikipedia defines Put-Call parity as: C - P = D(F - K) ---------------- C = call price P = put price F = *FORWARD* price K = strike which can be re-...
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0answers
63 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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0answers
41 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
63 views

Why do we need to borrow money in the call-put parity? [closed]

As I understand it, the call put parity is given by $$c = p + S - \frac{X}{(1 + r)^T}$$ I understand the rationale behind simultaneously buying the call, put and underlying asset for $S$, but why ...
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0answers
155 views

What are the main problems for calculating the implied volatility of in the money American put options?

As stated in the question I have a problem with calculating the implied volatility for in the money put options I have a data set of 2.6 million American style plain-vanilla call and put options. For ...
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2answers
206 views

Why do I get a curved line when I plot “implied interest rate” on the strike price?

Currently, I am working on my thesis (MSc. Finance) and I run into an interesting “phenomenon”. I have option data for a non-dividend paying stock. In class I have learned, how to calculate the ...
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0answers
58 views

Is it necessary for $P(K, t) - P(K + s, t) \geq se^{-rt}$ to hold?

Let $P(K, t)$ be a put option with strike price $K$ and expiration time $t$. Let $s > 0$. Is it necessarily true that the inequality $$P(K, t) - P(K + s, t) \geq se^{-rt}$$ holds? I know that ...
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1answer
85 views

How to get Forward price based on Put-Call parity?

Could you advise how to find a forward price using Call/Put (+Spot and Strike) ? Investodepia says that forward is equal to option's strike based on Put-Call Parity but it seems to me there is a ...
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1answer
317 views

Bermudan Swaption

Is there an equation of the kind of call-put parity for Bermudean swaptions ? (maybe an inequality ) Is there an intuitive description of what would be an optimal exercise moment ? Intuitively I ...
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2answers
73 views

Construct a portfolio of European call options with a certain payoff function

My question is similar to Replicate a Portfolio with Given Payoff but I am not quite sure how to apply this to my problem. A portfolio of European call options on an asset $S_T$ has a payoff ...
2
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1answer
88 views

Determine the maximum arbitrage profit from the given contracts

I really have tough time trying to figure this out. An investor observes the following prices in the market: Euro-Stoxx-Future DEC 148.02-148.03; Euro-Stoxx-Future Call-Option DEC 148.00 1.13-1.15; ...
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0answers
154 views

Implied Funding/Borrow Costs in Short-Dated ETF Option Prices

I'm struggling with some anomalous behavior in an analysis I'm running and was hoping for some advice/insights. I'm attempting to extract the implied funding/borrow costs from ETF option prices (say ...
2
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1answer
167 views

Should Put/Call Parity result in Zero Return or the Risk-Free Rate?

Sorry in advance if this is a basic question. I'm examining some potential at-the-money put/call arbitrage. What I found surprised me somewhat: ...
2
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1answer
131 views

Call Option Overvalued and put-call parity [closed]

I have a question regarding if a Call option is overvalued compared to the call price and how you can benefit from the Arbitrage opportunity. My thoughts are as follows: Step 1: Short the call ...
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1answer
117 views

Is there an advantage trading options based on deep in the money Open Interest Volume ratio

Problem: Deep in the money options contracts will be assigned at expiration date. Higher Volume ratio of deep in the money contracts at expiration calls or puts leads to day after expiration date we ...
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1answer
137 views

Decreasing value of the Put option with increasing Time to maturity [closed]

Can you think of a situation when increasing the time to maturity lowers the value of a put option? If yes, show the example pls.
2
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1answer
163 views

Risk of Put-Call-Parity in practice

When $C+PV(K) \ne P + S_0$, it's an opportunity for risk-free arbitrage (excluding cost). In practice, what potential risk could make the arbitrage fail? I know that failure to build complete ...
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1answer
129 views

Equity repo close to money market rates?

I've noticed that the repo rate (here I mean the effective financing rate of the forward position in stock) implied from synthetic forwards is almost the same as money market benchmark (XXXibor 3M) ...
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2answers
2k views

Put-call parity for cash settled swaptions

The Euro swaption market is changing from cash to physical settlement quotation in July 2018 $-$ see e.g. "Euro swaptions market prepares for pricign revamp (Risk, 2018)". When describing the issues ...
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3answers
774 views

Put Call Symmetry

I want to show the Put Call Symmetry without using the explicite Black Scholes formula. In other words I want to show Call(t, x, K, T) = Pull(t, K, x, T) where $S_t = x $ for $t \in [0, T]$. I ...
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0answers
66 views

Different versions of Put-Call Parity

Why is it stated sometimes that $C - P = F$ and in wikipedia it statest that $C - P = D(F-K)$, where D is the discount factor and K is the strike (of both the call and put?). Is this just affected ...
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0answers
462 views

Understanding put-call parity

I'm a person with math background trying to break into quantitative finance, and there's something about put-call parity that is not making sense to me. Below I'll detail my understanding of the ...
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1answer
335 views

Interpretation and intuition behind the Put-Call symmetry under the Heston Model

I am currently working on a report regarding the put-call symmetry relations under the Heston model. I did all the math and managed to prove the relations using PDE approach. However, I wish to have a ...
2
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1answer
345 views

Question about the vega of a stock

In Black-Scholes model with constant parameters, a call and a put with the same characteristics have the same vega: https://en.wikipedia.org/wiki/Black%E2%80%93Scholes_model#The_Greeks Using call-put ...
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0answers
286 views

Convexity of Call option prices using Put-Call parity relationship

I am trying to price vanilla options using a particular Bayesian approach that I have found in a paper. To do that I need to construct a likelihood function, approximating the tail of the distribution ...
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1answer
445 views

Violation of the call-put parity

The last price of Wells Fargo (Ticker: WFC) on Thursday, 10/26/17, was $55.62. Options with expiration 11/17/17 had following last prices: Options with expiration 11/17/17 had following last prices: ...
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2answers
218 views

Is an options implied dividends DCF model consistent with risk neutral/arbitrage-free valuation?

We're talking about how we price every financial instrument: by discounting the payoff, that is, we take future cash flows and we discount them by a proper rate which takes into account the risk of ...
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2answers
866 views

Implying risk-free rates using Put/Call parity

I recently purchased SPX options data from the CBOE. Normally, if the data is OK and the Put-Call parity holds, one should expect to correctly imply ZC (Zero Coupon bond) prices and forwards by ...
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1answer
259 views

Put-Call Parity on Currency and Binomial Trees

I tried solving the below problem without knowing the shortcut of thinking about this in terms of a put versus a call. I can't seem to arrive at the correct answer using my method and I'm wondering ...
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3answers
5k views

Relationship between forward and option prices

Do forward prices factor into option prices at all? It seems to me from Black-Scholes that you just need a spot price and interest rate r. I understand that $F_t = S_0 e^{r t}$, but I don't know if ...
4
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1answer
683 views

Build a Synthetic Loan for Personal Finance

Suppose I am short of cash and want a loan for some mundane objective like travelling or buying a car. The interest rate for personal loan with my bank is too high. Is there any way in finance that ...
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3answers
985 views

At the money put and call having the same price

This is a commonly asked question and I have not been able to find a satisfactory answer to it. Let me first phrase it here. Suppose that interest rates are $0$ and consider an at the money put and an ...
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1answer
154 views

How far the spot price is likely to go from the current level in three months if its volatility is 15.7%

On Page 24 of N. Taleb's "Dynamic Hedging" the author gives the following example Example: Assume that an asset trades at \$100, with interest rates at 6% (annualized) and volatility at 15.7%. ...
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2answers
609 views

Prove that the vertical spread condition is bounded

I need to prove that vertical spread is bounded, by using no arbitrage condition. 0 > (C(T,K1 )- C(T,K2))/(K1- K2 ) >-e^(-r*T ) I have documented my ...
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0answers
30 views

Best strategy for generating floats with minimum amount of risk

I'm looking for a way to get cash-in-hand in exchange for future obligation. For example, I can sell deep-in-the-money puts and buy out-of-the-money puts (for hedge) with expiration of 2 years, The ...
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1answer
79 views

Is it possible to calculate the call-put parity for an option's portfolio?

Let's say I have designed an option's portfolio. The portfolio includes long as well as short positions in European-style put and call contracts based on the same underlying asset with different ...
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1answer
168 views

Is this representation of the put-call parity correct? (Implied dividend estimation)

I am looking at implied dividend yields to be obtained from the put-call parity and have come across the following answer: Implied dividend estimation It states that $$ PV(div) = P - C + (S - K) + K(...
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1answer
114 views

Put call parity: when are the premiums the same?

Please explain why put call parity could be compared to the payoff of a long forward contract. ie. $C_E-P_E=V_X(0)$ where $C_E,P_E$ are the call/put premiums and $V_X(0)$ is the value of a long ...
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3answers
839 views

Construct option and stock portfolio

If a riskless security costs 100 today and will cost 120 at time T, a stock costs 50 today and will either be 70 or 30 at time T, and call options on the stock have strike price 50 expiring at time T, ...
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3answers
359 views

Put-Call Parity Application

In the binomial model, how that the Delta of a call option $\Delta^{call}$ and the Delta of a put option $\Delta^{put}$ with the same maturity and strike satisfy $$\Delta^{call}_t - \Delta^{put}_t = ...
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1answer
72 views

Understanding the necessary and sufficient conditions for rational early exercise of a call option

I am self-studying for an actuarial exam, and I encountered the following in my text: The author states that if $PV_{t, T}\text{(Divs)} < K(1 - e^{-r(T - t)})$, early exercise is not rational. ...
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4answers
3k views

Difficulty understanding put-call parity for currency options

I am self-studying for an actuarial exam on models for financial economics. I am having difficulty thinking about the put-call parity for currency options, specifically how use the notation. Here is ...