I just look at someone explanation what does it mean no arbitrage pricing. I am wondering whether it looks correct while I have some doubts if we assume that S is a stochastic process. If S is a deterministic process the subject does not look interesting. Arbitrage PricingSuppose we have a stock S and a cash bond with continuously compounded constant interest rate r. Let the stock price at time t = 0 be [$]S_0[$]. Consider a forward contract, where one of the two parties agrees to sell the otherthe stock at some future time T for the strike price k on which they agree now, that is, at t = 0. The forward price is actually independent of the stock movements between t = 0 and t = T, and is given by: k = [$]S_0[$] exp(rT) .The reason for this is arbitrage. Generally, arbitrage is a mechanism for making ?correct? market prices, known as arbitrage pricing. In its idealized form arbitrage means that, if the price of something is not ?correct?, i.e., it is not priced accordingto arbitrage pricing, there is a risk-free way of making profit. Thus, suppose a bank was offering a forward with a strike price k > [$]S_0[$] exp(rT). Then at t = 0 we could borrow [$]S_0[$] dollars by selling cash bonds, and purchase oneunit of stock. At time T we could sell our stock to that bank for k dollars, repay our debt, which is now [$]S_0[$] exp(rT), and make a risk-free profit of k −[$]S_0[$] exp(rT) dollars. Next, suppose a bank was offering a forward with a strike price k < [$]S_0[$] exp(rT). Then at t = 0 we could sell one unit of stock, and buy [$]S_0[$] worth of cash bonds. At time T our bonds are worth [$]S_0[$] exp(rT), and we could buy one unit of stock from [$]S_0[$] that bank for k dollars, hence making a risk-free profit of [$]S_0[$] exp(rT) − k dollars.

Yes, we typically teach this in the second lecture of an introductory derivatives class.

I do not against the standards but whether $1 invested in 3 month forwards: oil, Microsoft stock, gold and whether have equal forward delivery price?

QuoteOriginally posted by: list1I do not against the standards but whether $1 invested in 3 month forwards: oil, Microsoft stock, gold and whether have equal forward delivery price?The cash-and-carry arbitrage argument is pretty powerful, and the one thing it absolutely does not depend on is expected return, which usually confuses people. Possible complications include dividends, borrowing/shorting cost, storage cost, and indirect benefits from ownership (typically referred to as a convenience yield). None of this is relevant to non-storable "commodities" like volatility and weather, and is of limited value for things like natural gas and electricity, which are only somewhat storable.

O' k I also believe that cash-and-carry arbitrage argument is quite strong in finance. We are talking only on theoretical level.1. Whether does the pricing of the forward should be change if I assume that buyer has already cash say n[$]S_0[$], n = 1, 2, .. and does not need to make return payment to bank. What is reasonable price for the correspondent forward?2. In the theory we can assume that S is a random process with given distribution. One can assume that S is a GBM with known coefficients.There is a set of oil strikes in USD format: 45 , 50, 55, 60 in 3 month. What would be the fair spot prices for such forward contracts? whether does cash-and-carry no arbitrage pricing exists?

QuoteOriginally posted by: list1O' k I also believe that cash-and-carry arbitrage argument is quite strong in finance. We are talking only on theoretical level.1. Whether does the pricing of the forward should be change if I assume that buyer has already cash say n[$]S_0[$], n = 1, 2, .. and does not need to make return payment to bank. What is reasonable price for the correspondent forward?2. In the theory we can assume that S is a random process with given distribution. One can assume that S is a GBM with known coefficients.There is a set of oil strikes in USD format: 45 , 50, 55, 60 in 3 month. What would be the fair spot prices for such forward contracts? whether does cash-and-carry no arbitrage pricing exists?it would be helpful if you don't use phrases such as "spot prices for forward contract". Better to say just price as we will all know you are referring to the price of a forward with maturity T at time 0.Anyway, to answer your question on the prices of the forward contracts using cash and carry, assuming that the spot price of oil is S then the forward contract is worthS - Kexp(-rT) where K is the strike price. hth

QuoteOriginally posted by: daveangelQuoteOriginally posted by: list1O' k I also believe that cash-and-carry arbitrage argument is quite strong in finance. We are talking only on theoretical level.1. Whether does the pricing of the forward should be change if I assume that buyer has already cash say n[$]S_0[$], n = 1, 2, .. and does not need to make return payment to bank. What is reasonable price for the correspondent forward?2. In the theory we can assume that S is a random process with given distribution. One can assume that S is a GBM with known coefficients.There is a set of oil strikes in USD format: 45 , 50, 55, 60 in 3 month. What would be the fair spot prices for such forward contracts? whether does cash-and-carry no arbitrage pricing exists?it would be helpful if you don't use phrases such as "spot prices for forward contract". Better to say just price as we will all know you are referring to the price of a forward with maturity T at time 0.Anyway, to answer your question on the prices of the forward contracts using cash and carry, assuming that the spot price of oil is S then the forward contract is worthS - Kexp(-rT) where K is the strike price. hthDave, you are right. I thought that I could illustrate other point on pricing by using my example but it looks does not relevant for my goal. My point implies that cash-and-cary is somewhat incomplete. If S ( t ) is a random asset on [ 0 . T ] and we buy a forward at t = 0 with delivery at T > 0 then strike price k = [$]S_0[$] exp(rT) implies implies risk characteristics :a chance of profit / loss P { S ( T, [$]\omega[$] ) > k } / P { S ( T, [$]\omega[$] ) < k }average profit //// loss [$] avg_P\,( T ) \,=\, \int_{k}^{+ \infty}\, s \,P ( S ( T ) \, \in\, dy )[$] //// [$] avg_L\,( T ) \,=\, \int^{k}_{0}\, s \,P ( S ( T ) \, \in\, dy )[$]Standard deviation of the profit/loss can be written here.One can call the price k overpriced regardless whether it is cash-and-cary or other if [$] \frac{avg_P\,( T ) }{ avg_L\,( T )} < 1 [$] and underpriced if the latter fraction is larger than 1.There are many useful risk parameters can be used for market participants benefits. One can think that the right spot price is that when [$] \frac{avg_P\,( T ) }{ avg_L\,( T )} = 1 [$] Of course in many cases cash and carry price can be close and have similar dynamics but qualitatively these are different prices.My point is to illustrate more broader point on market pricing.

QuoteOriginally posted by: list1QuoteOriginally posted by: daveangelQuoteOriginally posted by: list1O' k I also believe that cash-and-carry arbitrage argument is quite strong in finance. We are talking only on theoretical level.1. Whether does the pricing of the forward should be change if I assume that buyer has already cash say n[$]S_0[$], n = 1, 2, .. and does not need to make return payment to bank. What is reasonable price for the correspondent forward?2. In the theory we can assume that S is a random process with given distribution. One can assume that S is a GBM with known coefficients.There is a set of oil strikes in USD format: 45 , 50, 55, 60 in 3 month. What would be the fair spot prices for such forward contracts? whether does cash-and-carry no arbitrage pricing exists?it would be helpful if you don't use phrases such as "spot prices for forward contract". Better to say just price as we will all know you are referring to the price of a forward with maturity T at time 0.Anyway, to answer your question on the prices of the forward contracts using cash and carry, assuming that the spot price of oil is S then the forward contract is worthS - Kexp(-rT) where K is the strike price. hthDave, you are right. I thought that I could illustrate other point on pricing by using my example but it looks does not relevant for my goal. My point implies that cash-and-cary is somewhat incomplete. If S ( t ) is a random asset on [ 0 . T ] and we buy a forward at t = 0 with delivery at T > 0 then strike price k = [$]S_0[$] exp(rT) implies implies risk characteristics :a chance of profit / loss P { S ( T, [$]\omega[$] ) > k } / P { S ( T, [$]\omega[$] ) < k }average profit //// loss [$] avg_P\,( T ) \,=\, \int_{k}^{+ \infty}\, s \,P ( S ( T ) \, \in\, dy )[$] //// [$] avg_L\,( T ) \,=\, \int^{k}_{0}\, s \,P ( S ( T ) \, \in\, dy )[$]Standard deviation of the profit/loss can be written here.One can call the price k overpriced regardless whether it is cash-and-cary or other if [$] \frac{avg_P\,( T ) }{ avg_L\,( T )} < 1 [$] and underpriced if the latter fraction is larger than 1.There are many useful risk parameters can be used for market participants benefits. One can think that the right spot price is that when [$] \frac{avg_P\,( T ) }{ avg_L\,( T )} = 1 [$] Of course in many cases cash and carry price can be close and have similar dynamics but qualitatively these are different prices.My point is to illustrate more broader point on market pricing.sorry - i have no idea what you are talking about.If you want to discuss investment theory then I would suggest that you read up on the body of literature first. Why does someone buy a stock or a bond ?the theory of financial derivatives is well developed as is the practice. there are many standard books on the subject.

QuoteOriginally posted by: daveangelQuoteOriginally posted by: list1QuoteOriginally posted by: daveangelQuoteOriginally posted by: list1O' k I also believe that cash-and-carry arbitrage argument is quite strong in finance. We are talking only on theoretical level.1. Whether does the pricing of the forward should be change if I assume that buyer has already cash say n[$]S_0[$], n = 1, 2, .. and does not need to make return payment to bank. What is reasonable price for the correspondent forward?2. In the theory we can assume that S is a random process with given distribution. One can assume that S is a GBM with known coefficients.There is a set of oil strikes in USD format: 45 , 50, 55, 60 in 3 month. What would be the fair spot prices for such forward contracts? whether does cash-and-carry no arbitrage pricing exists?it would be helpful if you don't use phrases such as "spot prices for forward contract". Better to say just price as we will all know you are referring to the price of a forward with maturity T at time 0.Anyway, to answer your question on the prices of the forward contracts using cash and carry, assuming that the spot price of oil is S then the forward contract is worthS - Kexp(-rT) where K is the strike price. hthDave, you are right. I thought that I could illustrate other point on pricing by using my example but it looks does not relevant for my goal. My point implies that cash-and-cary is somewhat incomplete. If S ( t ) is a random asset on [ 0 . T ] and we buy a forward at t = 0 with delivery at T > 0 then strike price k = [$]S_0[$] exp(rT) implies implies risk characteristics :a chance of profit / loss P { S ( T, [$]\omega[$] ) > k } / P { S ( T, [$]\omega[$] ) < k }average profit //// loss [$] avg_P\,( T ) \,=\, \int_{k}^{+ \infty}\, s \,P ( S ( T ) \, \in\, dy )[$] //// [$] avg_L\,( T ) \,=\, \int^{k}_{0}\, s \,P ( S ( T ) \, \in\, dy )[$]Standard deviation of the profit/loss can be written here.One can call the price k overpriced regardless whether it is cash-and-cary or other if [$] \frac{avg_P\,( T ) }{ avg_L\,( T )} < 1 [$] and underpriced if the latter fraction is larger than 1.There are many useful risk parameters can be used for market participants benefits. One can think that the right spot price is that when [$] \frac{avg_P\,( T ) }{ avg_L\,( T )} = 1 [$] Of course in many cases cash and carry price can be close and have similar dynamics but qualitatively these are different prices.My point is to illustrate more broader point on market pricing.sorry - i have no idea what you are talking about.If you want to discuss investment theory then I would suggest that you read up on the body of literature first. Why does someone buy a stock or a bond ?the theory of financial derivatives is well developed as is the practice. there are many standard books on the subject.1. i have no idea what you are talking about. /// In my simple formulas I tried to show the available market information regarding derivatives pricing which did not presented in standard books on the subject.2. Why does someone buy a stock or a bond ? /// I supposed that prices of stock and bonds are given without revealing intentions of its buy or sell reasons.

QuoteOriginally posted by: list11. i have no idea what you are talking about. /// In my simple formulas I tried to show the available market information regarding derivatives pricing which did not presented in standard books on the subject. that might be because they (i) wrong (ii) irrelevant (iii) ...Quote 2. Why does someone buy a stock or a bond ? /// I supposed that prices of stock and bonds are given without revealing intentions of its buy or sell reasons.no - wrong answer

bearish, Originally posted by: list1So, back when you embarked on your SSRN onslaught, one of your co-authors mentioned to me that you were looking for a job, and I thought the writing spree was a pretty credible marketing effort. Somewhat less so the business of picking fights with people on Wilmott, but be that as it may. Have you found a job yet?bearish, no

Cash-and carry no-arbitrage forward pricing is pretty basic. Here is a good url that explains in quite a bit of detail how it works:https://en.wikipedia.org/wiki/Forward_contractPlease pay particular attention to the section titled Rational Pricing, that section explains and applies the no-arbitrage argument. Now, the methodology presented there is old school in that it assumes no counterparty credit risk. But within the context of its assumptions it is a logical, consistent and complete model. And it has worked well enough to have been used in a variety of markets for decades.All kinds of people have been working at relaxing some of the unrealistic assumptions behind the classic no-arbitrage pricing models. Attempts to relax the mythical assumptions tend to result in considerably more complex models and introduces additional model risk. Sometimes people with bigger ideas make a fortune in this business. More often they fall away with their head handed to them on a platter. As an example, I vividly remember a certain Swiss bank calling comparatively tight markets in index amortizing swaps, claiming they had developed a better model with tighter hedging. A few quarters later after losing big money they realized they had put into production a model with a serious error. That particular market pretty much dried up entirely.

QuoteOriginally posted by: DavidJNCash-and carry no-arbitrage forward pricing is pretty basic. Here is a good url that explains in quite a bit of detail how it works:https://en.wikipedia.org/wiki/Forward_contractPlease pay particular attention to the section titled Rational Pricing, that section explains and applies the no-arbitrage argument. Now, the methodology presented there is old school in that it assumes no counterparty credit risk. But within the context of its assumptions it is a logical, consistent and complete model. And it has worked well enough to have been used in a variety of markets for decades.All kinds of people have been working at relaxing some of the unrealistic assumptions behind the classic no-arbitrage pricing models. Attempts to relax the mythical assumptions tend to result in considerably more complex models and introduces additional model risk. Sometimes people with bigger ideas make a fortune in this business. More often they fall away with their head handed to them on a platter. As an example, I vividly remember a certain Swiss bank calling comparatively tight markets in index amortizing swaps, claiming they had developed a better model with tighter hedging. A few quarters later after losing big money they realized they had put into production a model with a serious error. That particular market pretty much dried up entirely.I think that I understand cash-and-carry pricing. My point not to say that it is wrong and needed to be replaced by other theory. My point is to show that any spot price of the forward contract implies market risk. I do not want here to talk about credit risk . We can think that it is included in market risk or it should be considered separately. In standard liquid market with bis-ask spread to observe arbitrage opportunity is a very rare event nevertheless to loose or to get money during a short period is a quite frequent event. Unfortunately market risk formally does not represent itself in pricing and the only no arbitrage argument is used for theoretical pricing almost all classes of derivatives.

QuoteOriginally posted by: list1I think that I understand cash-and-carry pricing. My point not to say that it is wrong and needed to be replaced by other theory. My point is to show that any spot price of the forward contract implies market risk. I do not want here to talk about credit risk . We can think that it is included in market risk or it should be considered separately. In standard liquid market with bis-ask spread to observe arbitrage opportunity is a very rare event nevertheless to loose or to get money during a short period is a quite frequent event. Unfortunately market risk formally does not represent itself in pricing and the only no arbitrage argument is used for theoretical pricing almost all classes of derivatives.Whooot?

list1, not sure what you mean. BUT, in general you price something by how you can hedge it i.e. eliminating the market risk. if you understand cash and carry args then why are you trying to re-invent the wheel?