Introduction of Option Concept to Money
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Possession of currency is possession of option.

 Do you know option transaction? It is written in study guide that

 [Buying and selling of rights to buy or sell a certain amount of commodities or securities, on a predetermined day or within a period of time, at predetermined price (exercise price)].

 As it is buying and selling of rights, both to make a deal or not to make a deal are permitted to buyer. If the price is advantageous, right is exercised. If the price is disadvantageous, right is not exercised.
 Buyer of option pays option fee. Cost as payback of right is paid to seller of option. Seller of option must make a deal (be a partner of buyer) on the condition of option when option is exercised by buyer. As payback of it, seller of option can get option fee.

 To hold money is to hold right to be able to buy services freely. Therefore, to hold money is to hold a kind of option.

 Owner of option pays option fee as payback of the right.
 If to hold money is assumed to hold option, money holder must pay option fee depending on the amount and the period.

 Suppose, for instance, option fee to hold ¥100 for a day is ¥1.

 Today ¥100 --> Tomorrow ¥99 ( Pay option fee ¥1 )
            Day after next ¥98.01 (In addition, pay option fee ¥0.99)

 If to hold money is assumed to hold option, as just described, amount decreases as time passed.

 In this case, because amount decreases, change ratio of amount of money is minus.

 For these reasons, if change ratio of amount of money is assumed to be interest rate, application of minus interest rate is needed for possession of money. (In order to pay option fee.)

 In my book [Introduction of minus interest rate], it is explained that introduction of minus interest rate is necessary for economic theory. Main points of the book are described below.

1. Value of currency occurs only at the moment of economic transaction. In this
  case, amount of economic transaction corresponds to amount of currency.
  (Same amount, reverse direction flow.)
2. Change ratio of scale of economic transaction corresponds to that of amount of
  currency perfectly. (This is conclusion of the premise of 1). This means that
  (nominal) economic growth rate corresponds to interest rate perfectly.
3. If change ratio of scale of economic transaction doesn’t correspond to that of
  amoun of money, economic transaction can’t be realized.
4. If (nominal) economic growth rate is minus, interest rate needs to be minus.

 As described above, needs for minus interest rate have been explained sufficiently, but it is not clear to introduce these points to economic theory / system. Prime reason may be that experts can’t sufficiently understand the reason for interest rate to be minus. (Prevalence of electronic money is needed for introduction of minus interest rate. (Privately owned paper money and coin etc. can’t be decreased ))

 Contents of this text is much more comprehensible explanation of necessity for introduction of minus interest rate. If possession of currency is assumed to buy option, it is quite natural that interest rate becomes minus to pay option fee.

 If excess debt is burdened, level of interest rate should be nominal economic growth rate or less.

 The opinion [(nominal) economic growth rate corresponds to interest rate.] is on the premise that [value of currency occurs only at the moment of making a deal.]. If value of currency occurs at the moment of not making a deal, this opinion is not applied.

 In present Japan, debts of central and local governments are over 1000 trillion yen. This means that huge currency (credit / debt) that has value at the moment of not making a deal occurs. How should the level of interest rate be decided under this condition.

 As the premise is [value of currency occurs only at the moment of making a deal.], (nominal) economic growth rate should be applied to change rate (level of interest rate) of amount of money used in economic transaction.
 In addition, option fee occurs in currency not used in economic transaction. Therefore, level of interest rate that should be applied to the currency is minus interest rate.

 Amount of currency of the former is defined as A, Amount of currency of the latter is defined as B. If each level of interest rate of both A and B is defined as r(A) and r(B), level of interest rate that should be applied to whole currency is defined as follows.

 R = { A × r(A) + B × r(B) } ÷ ( A + B )

 As r(B) is minus, R is smaller than R(A) (nominal economic growth rate).

 As described above, it is concluded that level of interest rate needs to be far lower than nominal economic growth rate in present Japan that has huge debts.

 The opinion [(nominal) economic growth rate should correspond to interest rate.] is not applied to present Japan. It is necessary for interest rate to be lowered further in order to revive Japanese economy.

Attention: Because nominal economic growth rate in this book includes all economic transactions, it doesn’t correspond to change ratio of GDP perfectly. (This has been written in [Introduction of Minus Interest Rate.])

Feb 2007.


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