From the design philosophy of MOV stable currency to see the macro-control based on four factors

On January 15th, Bytom released the "MOV White Paper on Stable Financial System", which pioneered a three-level clearing system and introduced a risky bond clearing method, an all-weather risk measurement body, and a risk rating model based on the Markov chain. At the same time, the team also launched the "Interpretation of the Bytom MOV Stability Financial System White Paper" activity, which was actively participated by fans in the community. This article is compiled from articles published by fans gentledog.

The MOV white paper mentions intervention and macro-control based on four factors C, R, P, and T, which respectively represent mortgage assets and credit (Collateral+Credit), risk intervention, stable currency prices, and stable currency circulation, and have the formula CR =PT. Here C, P, and T are easy to understand and can be quantified, but risk intervention R is not intuitive, and there is no clear definition in the white paper. I looked up some information, and I couldn't find the source of this formula, which is really puzzling. Here I build a model according to my own understanding, give the quantitative standard of risk intervention R, and try to explain the rationality of the formula.

brown sport

rememberSport for Brown. rememberfirst hit for brown sportthe moment of

A set of separate Brown campaigns and first hitsandand,here

Theorem 1

Constant A, B>0,

See the relevant textbook for proof.

rememberfor the Brown campaignhitmoment.

Theorem 2

Constant A, B>0,

Proof: According to the Markov property of the Brown motion,

in time periodThe Brown movements within are independent of each other.

May wish to

replaced by a set of independent variables

then,。

then,

(depending on independence)

The other formula can be proved in the same way.

Brown Movement with Barrier

Definition 1

set constant, sufficiently smallFor such a movement:

existexistWhen going up, make a Brown movement;

2. At a certain momenthour,hour,instant decrease, at the same time a negative shock is produced, the shock magnitude is；

3. At a certain momenthour,hour,instant increase, at the same time a positive shock is produced, the shock magnitude is；

then calledforas the upper barrier, withBrown movement for the lower barrier.

Definition 2

suppose at some pointhour, set at timeto timeAfter the first hit of A before spawning

The sum of positive shocks is(including timeimpact at the place),

its distribution function。

Correspondingly, the sum of negative shocks can be definedand its distribution function。

make

makehour,

whenhour,

From this you can getThe sum of the positive shocksand its distribution function is

Its probability density function is，

Its expected value is，

When talking about impact below, the default issituation.

Modeling and Analysis

Assuming that the price of the stable currency does a geometric Brownian movement when there is no intervention, the stable currency operator willbuy everywhere

single insell order at , the price at time t is。

Taking the logarithm of the price, suppose

，

forby

byhere

hereis a constant.

From the previous section, the sum of positive shocks can be defined accordinglyand its distribution function。

Definition 3

risk intervention

Easy to know,

。

examples and explanations

Risk Intervention R represents the average financial pressure on stablecoin operators when encountering each wave of stablecoin sell-offs.

For example, suppose there are 10 million stablecoins with a face value of 1 yuan in the market, and the stablecoin operators have only 7 million yuan in their hands. If all funds are used to repurchase stablecoins, then only 70%. In order to ensure the absolute stability of the system, a reasonable approach is that the operator places a sell order at 1 yuan and a buy order at 0.7 yuan. At this time, the average financial pressure encountered by operators during each wave of stablecoin selling is 1/0.7=1.42857 times.